{"id":15,"date":"2023-09-17T11:10:24","date_gmt":"2023-09-17T11:10:24","guid":{"rendered":"https:\/\/mathority.org\/id\/komposisi-fungsi-fungsi-komposit\/"},"modified":"2023-09-17T11:10:24","modified_gmt":"2023-09-17T11:10:24","slug":"komposisi-fungsi-fungsi-komposit","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/komposisi-fungsi-fungsi-komposit\/","title":{"rendered":"Komposisi fungsi (fungsi gabungan)"},"content":{"rendered":"<p>Pada artikel ini, kami akan menjelaskan apa itu fungsi komposit (atau komposisi fungsi). Selain itu, Anda akan dapat melihat beberapa contoh fungsi gabungan dan cara menghitung domain fungsi jenis ini. Terakhir, Anda akan menemukan properti komposisi fungsi dan beberapa latihan langkah demi langkah untuk dipraktikkan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-composicion-de-funciones\"><\/span> Apa itu komposisi fungsi?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Komposisi fungsi terdiri dari evaluasi <strong>secara berturut-turut<\/strong> nilai yang sama dari variabel bebas (x) dalam dua fungsi atau lebih.<\/strong> Misalnya, menyusun fungsi (gof)(x) menghasilkan fungsi komposit g[f(x)]. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/composition-des-fonctions.webp\" alt=\"komposisi fungsi\" class=\"wp-image-637\" width=\"319\" height=\"115\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Ekspresi fungsi komposit<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e3eba5c152156d18705b3afd68f487e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\circ f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\"><\/p>\n<p> kita membaca \u201cf disusun dengan g\u201d atau \u201cf diikuti oleh g\u201d.<\/p>\n<p> Perhatikan bahwa urutan penting dalam komposisi fungsi, fungsi di sebelah kanan simbol komposisi diterapkan terlebih dahulu<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-876a58c2d2bc4ab866c0af7a5cdbf4b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(f)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"22\" style=\"vertical-align: -5px;\"><\/p>\n<p> lalu fungsinya di sebelah kiri simbol komposisi <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6c9247c09d7827160e8316d83ce2b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(g).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-composicion-de-funciones\"><\/span> Contoh komposisi fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Mengingat definisi fungsi komposit, mari kita lihat contoh cara menghitung komposisi dua fungsi.<\/p>\n<ul>\n<li> Mengingat dua fungsi berbeda berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9c8e90e6e8bb1e0837f424caaf5d1a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x+1 \\qquad g(x)=\\cfrac{x+4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"243\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Hitung fungsi gabungan<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-624e8051bd11c44546f1270c91d069ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan mengevaluasinya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf60bc9fcf312a246a055c15ee98033c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Komposisi fungsi<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-624e8051bd11c44546f1270c91d069ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> Ini berarti kita perlu melakukan fungsi komposit berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb23add9f37be01b1ebf5923aef845ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x) = g\\Big(f(x)\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"162\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Untuk mengatasinya kita ganti<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> dengan ekspresi aljabarnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-179039983ee415873b7367ac255c1023_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(f(x)\\Big)= g\\Big(3x+1\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"166\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p> Dan sekarang kita mengambil fungsi dari<em> <\/em><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d124ddf8086d5d941fcb1de7c075c0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=\\cfrac{x+4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<p>dan kami memasang ekspresi<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4b24384ffd361d326faea85da151496_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -2px;\"><\/p>\n<p> dimana ada satu<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-845f2902b8bebf60c3c7372a7fbe4d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9407b8a097013423f71626368a65940b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(3x+1\\Big)=\\cfrac{(3x+1)+4}{2}=\\cfrac{3x+5}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"275\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dengan cara ini kita telah menghitung fungsi <em>f<\/em> yang terdiri dari <em>g<\/em> :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b46e81ab3496bd4daad7560eabda1caa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x)=\\cfrac{3x+5}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"152\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Terakhir, untuk mengevaluasi fungsi komposit di<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<p> Cukup hitung gambar fungsi dalam nilai tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1a5472ce52fe01b6809224912a25539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(3)=\\cfrac{3\\cdot 3+5}{2}=\\cfrac{14}{2}=7\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"237\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"dominio-de-la-funcion-compuesta\"><\/span> Domain fungsi komposit<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Biasanya, ketika kita melakukan operasi pada suatu fungsi, domain dari fungsi yang dihasilkan adalah perpotongan domain dari fungsi aslinya. Namun sifat ini tidak dipenuhi oleh komposisi fungsi.<\/p>\n<p> <strong>Domain komposisi fungsi<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1e321d1fe5674142070eefd17519b77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(g\\circ f)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p> ekuivalen dengan himpunan semua nilai x pada domain fungsi<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> seperti<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> termasuk dalam domain fungsi<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dce98a79808d5694e9c7a9f4545e45f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf27df12b66bbfdc7516fe47410cbf5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom}(g\\circ f)=\\{x\\in\\text{Dom}(f)\\ | \\ f(x)\\in \\text{Dom}(g)\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, untuk menghitung domain suatu fungsi komposit, pertama-tama Anda harus mencari domain masing-masing fungsi secara terpisah, lalu domain fungsi yang dihasilkan dari operasi tersebut. Dengan demikian, domain komposisi fungsi akan terdiri dari semua nilai yang memenuhi kondisi matematika sebelumnya.<\/p>\n<p> \ud83d\udc49 Ingat, jika kamu menemui masalah yang kamu tidak tahu cara mengatasinya, kamu bisa bertanya kepada kami di kolom komentar di bawah! <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-composicion-de-funciones\"><\/span> Sifat komposisi fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fungsi komposit mempunyai ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> Komposisi fungsi mempunyai sifat asosiatif, oleh karena itu persamaan berikut selalu benar:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdfe1df3ab8d42f8d2af7f0d33628dba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\circ (g\\circ h)=(f\\circ g)\\circ h\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"178\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Secara umum komposisi fungsi tidak bersifat komutatif, sehingga urutan operasi menentukan hasilnya:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a641ded39b05f710e2cbc89f7c309275_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\circ g\\neq g\\circ f\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> Unsur netral susunan fungsi berhubungan dengan fungsi identitas\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da6458e64d1478ad56231146ce88db89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p> Jadi, setiap fungsi yang disusun dengan fungsi identitas menghasilkan fungsi itu sendiri:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-161782350ae4c16617cbe0795e0fa35a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\circ id = id \\circ f = f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"143\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5ce8a7d2dbca796654cb483808271e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"id = x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Menghitung invers komposisi dua fungsi sama dengan mencari invers masing-masing fungsi terlebih dahulu, lalu menentukan fungsi kompositnya:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e5f9cc891e8322cf737caf8fa76a92f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(f\\circ g)^{-1}=f^{-1}\\circ g^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Fungsi invers juga berperan sebagai elemen simetris dari fungsi majemuk, karena komposisi suatu fungsi dengan inversnya ekuivalen dengan fungsi identitas:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b801f112fdb719fad2b8c605ad831f0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(f\\circ f^{-1})^{-1}=(f^{-1}\\circ f)=id=x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"254\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Turunan komposisi dua fungsi dihitung menggunakan aturan rantai:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-edf8bcb549ad025afce59e50c1cfbb94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(g\\circ f\\bigr)'(x)=g'\\Bigl(f(x)\\Bigr)\\cdot f'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"223\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/rantai-aturan-turunan\/\">apa aturan rantainya?<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-composicion-de-funciones\"><\/span> Latihan soal komposisi fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Mengingat dua fungsi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d22ce1010c1d1f2baa34bd5b96e4ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x-2 \\qquad g(x)= 5x + 4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Hitung komposisi fungsi <em>f<\/em> yang tersusun dengan <em>g<\/em> dan <em>g<\/em> yang tersusun dengan <em>f<\/em> . <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1e321d1fe5674142070eefd17519b77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(g\\circ f)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e664a72ceacc815125057558ab04c6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(f\\circ g)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Komposisi fungsi<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-624e8051bd11c44546f1270c91d069ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> berarti menghitung fungsi komposit berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb23add9f37be01b1ebf5923aef845ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x) = g\\Big(f(x)\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"162\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi untuk mengatasinya kita ganti<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> untuk ekspresinya:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cc434b7ab7aea14a249be3943671119b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-13cb5a87becd27ff70f8fb5fb3b13239_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(f(x)\\Big)= g\\Big(x-2\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"157\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> DAN<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf53f7369c2b0dfc1c60397d3dab8cd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(x-2\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"68\" style=\"vertical-align: -11px;\"><\/p>\n<p> Artinya dalam ungkapan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a63a5d2293c895c25f8684ae82cefbf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x) =5x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<p> Anda perlu mengganti variabel<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Untuk<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f860e374f2a5f611e892f304ee0cc2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-575d7c9f8dde8d78c1dd910ba1557ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(x-2\\Big) = 5(x-2) +4= 5x-10+4 = 5x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"374\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Belum:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df045f4ebc5cdfdcbd99a12307235058_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\left(g \\circ f\\right)(x) = 5x-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Di sisi lain, untuk mencari fungsi <em>g<\/em> yang terdiri dari <em>f<\/em> Anda harus melakukan prosedur yang sama tetapi dengan urutan terbalik:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e9be8f1bab4b7607441c7c1b7e3ad0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\left(f \\circ g\\right)(x)&amp;= f\\Big(g(x)\\Big)\\\\[2ex]&amp;=f\\Big(5x+4\\Big)\\\\[2ex]&amp;=(5x+4)-2\\\\[2ex]&amp;=\\bm{5x+2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"167\" width=\"193\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Latihan ini juga menunjukkan sifat bahwa fungsi komposit tidak bersifat komutatif, karena hasilnya bergantung pada urutan penerapan fungsi tersebut.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 2<\/h3>\n<p> Mengingat dua fungsi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e7ff3894ffbafb8d56296b5b3d0a080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x) =x^2-3 \\qquad g(x)=\\frac{2x+3}{x+4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"251\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Menghitung komposisi fungsi <em>f<\/em> yang disusun dengan <em>g<\/em> . <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1e321d1fe5674142070eefd17519b77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(g\\circ f)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Fungsi <em>f<\/em> yang terdiri dari <em>g<\/em> berarti menyelesaikan fungsi gabungan berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb23add9f37be01b1ebf5923aef845ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(x) = g\\Big(f(x)\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"162\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami mengganti fungsi f(x) dengan ekspresinya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-28b41bd35ba991a996cf3a890aaeadf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(f(x)\\Big)= g\\Big(x^2-3 \\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"165\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang kita harus menggantinya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Untuk<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce3abcbe3e7405ea80705e3c169ae20d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalam ekspresi fungsi g(x):<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf0bb412f9088845027b57d83a91073d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}g\\Big(x^2-3\\Big)&amp;=\\cfrac{2(x^2-3)+3}{(x^2-3)+4}\\\\[2ex]&amp;=\\cfrac{2x^2-6+3}{x^2+1}\\\\[2ex]&amp;=\\cfrac{2x^2-3}{x^2+1}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"175\" width=\"206\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Singkatnya, hasil komposisi fungsinya adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d625dc7f6b8e7af0988037119d473f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\left(g \\circ f\\right)(x) =} \\cfrac{\\bm{2x^2-3}}{\\bm{x^2+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"155\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Diketahui dua fungsi kuadrat berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a594c87e42327318112e78714904aa81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x) =x^2 \\qquad g(x)=g(x)= x^2-4x+8\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"314\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Tentukan hasil komposisi fungsi berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b7186993d7a14fceff2669b6d3f10585_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(g\\circ f)(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-706bfe49f02e183102e665a522eb803c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> terdiri dari mencari fungsi komposit berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-217743a7af2baefbc83e1c377f3f804f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(2) = g\\Big(f(2)\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"160\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi untuk menyelesaikan fungsi komposit kita hitung dulu <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7bd87dc0308123b84fbe51bb86e0b009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2) :\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3421a45cc1c0ad35b18520e81ddc031_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-671b30c79ed994c1923982d4a09d2eae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2)=2^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, sebagai <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69585295dd3a781afd9ebde9750865bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2)=4 :\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f64414212eaa56a80be0b0ac9bd1be23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(g \\circ f\\right)(2) = g\\Big(f(2)\\Big) = g\\big(4\\big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"218\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi untuk mencari nilai fungsi komposit Anda tinggal menghitungnya saja <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e05e67fe2bbccdbd12d182052a93df62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(4) :\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9fc21e0e44e696ed36cd6e9a535cff09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\left(g \\circ f\\right)(2)&amp;=g\\Big(f(2)\\Big)\\\\[2ex]&amp;= g\\big(4\\big)\\\\[2ex]&amp;=4^2-4\\cdot 4+8 \\\\[2ex]&amp;= 16 - 16 + 8\\\\[2ex]&amp;= 8\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"198\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ringkasnya, hasil dari soal komposisi fungsi adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8d3e091b61117ac43ec8d17d4aa1d5b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\left(g \\circ f\\right)(2) =8}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Mengingat dua fungsi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0dabd181964a078fe5348b19efc168d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x-2}{-x+7}\\qquad g(x)= x^2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"256\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Tentukan hasil <em>g<\/em> yang disusun dengan <em>f<\/em> di x=2: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-47390afb10cf5e3de6b0ff87edeff73b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(f\\circ g)(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dalam hal ini, kita harus menghitung fungsi komposit berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6de0edda1d8a4151fc88faa013a012e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(f \\circ g\\right)(2) = f\\Big(g(2)\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"160\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi pertama-tama kita temukan <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-809314c764c52d861c5b9671f5139d5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(2) :\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4f1e7070d6f986eac4f1483f9a30198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94e98ec0f41ba6635ee79cf96968e7ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(2)=2^2-1=4-1 = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, seperti <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82da28e3a6fb3ea74c8e8ef8d022b202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(2)=3 :\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfe82e73b68c3b618cb0795bb6530af7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(f \\circ g\\right)(2) = f\\Big(g(2)\\Big) = f\\big(3\\big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"219\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi untuk menyelesaikan fungsi komposit kita perlu menghitung <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6d1361868e53506ddeca640a71aa321_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3) :\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9ec461a36a477af7bc703fd48bc3d4c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\left(f \\circ g\\right)(2)&amp;=f\\Big(g(2)\\Big)\\\\[2ex]&amp;= f\\big(3\\big)\\\\[2ex]&amp;=\\cfrac{2\\cdot 3-2}{-3+7}\\\\[2ex]&amp;=\\cfrac{6-2}{-3+7}\\\\[2ex]&amp;=\\cfrac{4}{4}\\\\[2ex]&amp;=1\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"305\" width=\"162\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kesimpulannya, hasil pelaksanaan fungsi majemuk adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8860734e1b816965b945b8ddf117912d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\left(f \\circ g\\right)(2)=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 5<\/h3>\n<p> Mengingat tiga fungsi berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cde9a25a0c078e5e4491aef0682310d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x+1 \\qquad g(x)= 3x - 5\\qquad h(x) = \\sqrt{x} - 3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"389\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Hitung komposisi 3 fungsi berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ff91e1d3fdea1de8b629e4c17cee6fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(h \\circ g \\circ f )(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ekspresi<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf14fee9bc19b3aaefabcac820afb69b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(h \\circ g \\circ f\\right)(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<p> Artinya kita harus menghitung fungsi komposit berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6525a7b5ac0a86cc710225df5ebdf7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(h \\circ g \\circ f\\right)(x) = h \\bigg( g\\Big(f(x)\\Big) \\bigg)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"225\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi pertama-tama kita tentukan <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0efee4b8fc162ee4ee30c15f1dac01c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big( f(x)\\Big):\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"74\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0ab9465f2aebf9fb7c81298eab5b8ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}g\\Big( f(x)\\Big)&amp;=g\\Big(x+1 \\Big)\\\\[2ex]&amp;= 3(x+1)-5\\\\[2ex]&amp;= 3x+3-5\\\\[2ex]&amp;= 3x-2\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"154\" width=\"181\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang kita menghitung<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0512ac0197a64c0dce8e3a14b97efd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h \\bigg( g\\Big(f(x)\\Big) \\bigg)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"98\" style=\"vertical-align: -17px;\"><\/p>\n<p> . Untuk melakukan ini, kami mengganti ekspresi yang ditemukan dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fde695528fc22ce481c7750cd392927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\\Big(f(x)\\Big)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"62\" style=\"vertical-align: -11px;\"><\/p>\n<p> di mana muncul<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalam fungsinya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-240be4d8f4d59436eb46fefb7d2f7633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h(x):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89fbb7189eaf2dd3c622466c7313806d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}h \\bigg( g\\Big(f(x)\\Big) \\bigg)&amp;= h \\bigg(3x-2\\bigg)\\\\[2ex]&amp;= \\sqrt{3x-2} - 3\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"83\" width=\"220\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kita tidak dapat menyederhanakan fungsi komposit lebih jauh lagi. Oleh karena itu, komposisi ketiga fungsi tersebut menghasilkan fungsi yang tidak rasional: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3d99aa6d620db9304fa7121387dfd95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\left(h \\circ g \\circ f\\right)(x) =\\sqrt{3x-2} - 3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini, kami akan menjelaskan apa itu fungsi komposit (atau komposisi fungsi). Selain itu, Anda akan dapat melihat beberapa contoh fungsi gabungan dan cara menghitung domain fungsi jenis ini. Terakhir, Anda akan menemukan properti komposisi fungsi dan beberapa latihan langkah demi langkah untuk dipraktikkan. Apa itu komposisi fungsi? Komposisi fungsi terdiri dari evaluasi secara &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/komposisi-fungsi-fungsi-komposit\/\"> <span class=\"screen-reader-text\">Komposisi fungsi (fungsi gabungan)<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[49],"tags":[],"class_list":["post-15","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This 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