{"id":3529,"date":"2025-07-25T13:00:00","date_gmt":"2025-07-25T06:00:00","guid":{"rendered":"https:\/\/example.com\/?p=3529"},"modified":"2025-07-28T17:09:38","modified_gmt":"2025-07-28T10:09:38","slug":"fungsi-komposisi","status":"publish","type":"post","link":"https:\/\/staging-blog.sirogu.com\/blog\/fungsi-komposisi","title":{"rendered":"Belajar Fungsi Komposisi &#038; Contohnya, Lengkap! | Matematika Kelas 10"},"content":{"rendered":"<p style=\"text-align: justify;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Fungsi%20Komposisi.png\" alt=\"Fungsi Komposisi\" width=\"820\" \/><\/p>\n<blockquote>\n<p style=\"text-align: center;\"><em>Kamu sudah tahu belum apa yang dimaksud dengan fungsi komposisi? Kalau belum, yuk, kita pelajari bersama melalui <strong><a href=\"https:\/\/www.ruangguru.com\/blog\/c\/matematika\/matematika-sma-kelas-10\">artikel Matematika kelas 10<\/a><\/strong> ini! Ada contoh soalnya juga, lho!<\/em><\/p>\n<p style=\"text-align: center;\">&#8212;<\/p>\n<\/blockquote>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Kamu pasti sudah tidak asing dengan istilah fungsi, kan? <strong>Fungsi adalah relasi <a href=\"\/blog\/matematika-kelas-7-hubungan-antarhimpunan-matematika\" rel=\"noopener\">himpunan<\/a> A ke himpunan B<\/strong>, dengan <strong>setiap anggota A dipasangkan ke tepat satu anggota B<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Fungsi sendiri dapat diilustrasikan seperti gambar berikut:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/fungsi.png\" alt=\"fungsi\" width=\"250\" \/><\/p>\n<p style=\"text-align: center;\">Contoh fungsi (Sumber: wikimedia.org)<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Nah, selain <strong><a href=\"\/blog\/apa-itu-relasi-dan-fungsi\" rel=\"noopener\">fungsi<\/a> <\/strong>ada juga nih, yang namanya fungsi komposisi. Wah, kayak gimana tuh? Penasaran, kan? Yuk, simak pembahasannya pada artikel berikut!<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"font-size: 18pt;\">Pengertian Fungsi Komposisi<\/span><\/h2>\n<p style=\"text-align: justify;\">Fungsi komposisi adalah <strong>fungsi yang melibatkan lebih dari satu fungsi<\/strong>. Ketika ada suatu fungsi, kemudian dilanjutkan dengan fungsi lainnya, maka akan membentuk suatu fungsi baru. Fungsi baru inilah fungsi hasil komposisi dari kedua fungsi sebelumnya.<\/p>\n<p style=\"text-align: justify;\">Misalnya, ada fungsi f(x) dan g(x). Nah, fungsi f komposisi g adalah fungsi yang dipetakan oleh fungsi g(x) kemudian dilanjutkan oleh fungsi f(x). Operasi fungsi komposisi biasa dilambangkan dengan &#8220;o&#8221; dan dibaca komposisi atau bundaran.<\/p>\n<p style=\"text-align: justify;\"><strong>Baca Juga: <a href=\"\/blog\/apakah-fungsi-invers-itu\" rel=\"noopener\">Apakah Fungsi Invers Itu?<\/a><\/strong><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"font-size: 18pt;\">Bentuk-Bentuk Fungsi Komposisi<\/span><\/h2>\n<p style=\"text-align: justify;\">Misalnya ada fungsi f(x) dan g(x), maka fungsi komposisi yang dapat terbentuk dari f(x) dan g(x) adalah:<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">1. (f o g)(x)<\/span><\/h3>\n<p style=\"text-align: justify;\">(f o g)(x) dapat dibaca \u201cfungsi f komposisi g\u201d atau \u201cf bundaran g\u201d, yang artinya <strong>fungsi yang dipetakan oleh fungsi g(x) kemudian dilanjutkan oleh fungsi f(x)<\/strong>. Jadi, fungsi g nya dikerjakan terlebih dahulu, kemudian hasilnya dimasukkan ke dalam fungsi f. Sehingga, dapat dinotasikan sebagai berikut:<\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt;\">(f o g)(x) = f(g(x))<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: justify;\"><span style=\"font-size: 14pt;\">2. (g o f)(x)<\/span><\/h3>\n<p style=\"text-align: justify;\">(g o f)(x) dapat dibaca \u201cfungsi g komposisi f\u201d atau \u201cg bundaran f\u201d, yang artinya <strong>fungsi yang dipetakan oleh fungsi f(x) kemudian dilanjutkan oleh fungsi g(x)<\/strong>. Kalau g o f, yang dikerjakan terlebih dahulu adalah fungsi f, kemudian dilanjutkan atau dimasukkan dalam fungsi g. Sehingga, dapat dinotasikan sebagai berikut:<\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt;\">(g o f)(x) = g(f(x))<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Agar lebih mudah memahami, kamu bisa perhatikan contoh fungsi komposisi pada gambar berikut:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Contoh%20Fungsi%20Komposisi.png\" alt=\"Contoh Fungsi Komposisi\" width=\"600\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Dari gambar di atas, dapat kita peroleh:<\/p>\n<p style=\"text-align: justify;\">Jika f : A \u2192 B ditentukan dengan rumus f(x) dan g : A \u2192 B ditentukan dengan rumus g(x), maka hasil dari f komposisi g adalah h(x) = (g o f)(x) = g(f(x)).<\/p>\n<p style=\"text-align: justify;\"><strong>Baca Juga: <a href=\"\/blog\/perbedaan-persamaan-linear-dan-pertidaksamaan-linear\" rel=\"noopener\">Perbedaan Persamaan Linear dan Pertidaksamaan Linear<\/a><\/strong><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"font-size: 18pt;\">Sifat-Sifat Fungsi Komposisi<\/span><\/h2>\n<p style=\"text-align: justify;\">Fungsi komposisi memiliki sifat-sifat yang bisa kamu lihat pada gambar di bawah ini:<\/p>\n<p style=\"text-align: justify;\">Jika f : A \u2192 B , g : B \u2192 C , h : C \u2192 D, maka berlaku:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Sifat-Sifat%20Fungsi%20Komposisi.png\" alt=\"Sifat-Sifat Fungsi Komposisi\" width=\"600\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Oke, sekarang kita coba kerjakan contoh soal di bawah ini yuk, supaya kamu semakin paham dengan fungsi komposisi!<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: justify;\"><span style=\"font-size: 18pt;\">Contoh Soal Fungsi Komposisi<\/span><\/h2>\n<p style=\"text-align: justify;\">1. Diketahui f(x) = 2x + 5 dan g(x) = 3x &#8211; 7, maka (f o g)(x) adalah \u2026.<\/p>\n<p style=\"text-align: justify;\"><strong>Pembahasan:<\/strong><\/p>\n<p style=\"text-align: justify;\">Diketahui:<\/p>\n<p style=\"text-align: justify;\">f(x) = 2x + 5<\/p>\n<p style=\"text-align: justify;\">g(x) = 3x &#8211; 7<\/p>\n<p style=\"text-align: justify;\">Ditanya:<\/p>\n<p style=\"text-align: justify;\">(f o g)(x)?<\/p>\n<p style=\"text-align: justify;\">Jawab:<\/p>\n<p style=\"text-align: justify;\">(f o g)(x) = f(g(x))<\/p>\n<p style=\"text-align: justify;\">(f o g)(x) = 2g(x) + 5<\/p>\n<p style=\"text-align: justify;\">(f o g)(x) = 2(3x &#8211; 7) + 5<\/p>\n<p style=\"text-align: justify;\">(f o g)(x) = 6x &#8211; 14 + 5<\/p>\n<p style=\"text-align: justify;\">(f o g)(x) = 6x &#8211; 9<\/p>\n<p style=\"text-align: justify;\">Jadi, (f o g)(x) = 6x &#8211; 9<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Baca Juga: <a href=\"\/blog\/matematika-kelas-10-membuat-fungsi-kuadrat-dari-grafik\" rel=\"noopener\">Cara Menyusun Persamaan dari Grafik Fungsi Kuadrat<\/a><\/strong><\/p>\n<p style=\"text-align: justify;\">Itu dia penjelasan tentang fungsi komposisi. Gimana? Sekarang, kamu sudah jauh lebih paham kan tentang fungsi komposisi? Jangan lupa untuk terus berlatih soal-soal lainnya, ya! Kamu juga bisa mempelajari lagi materi ini melalui <strong><a href=\"https:\/\/www.ruangguru.com\/ruangbelajar\" target=\"_blank\" rel=\"noopener\">ruangbelajar<\/a><\/strong>. Belajar kamu jadi makin seru dengan menonton video animasi lengkap dengan latihan soal dan rangkumannya juga. Gabung sekarang, yuk!<\/p>\n<p><a href=\"https:\/\/bayar.ruangguru.com\/\"><img decoding=\"async\" class=\"aligncenter size-medium\" src=\"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/ceb472c4-1feb-4a1d-afdf-4f92234a63d0.jpg\" alt=\"CTA Ruangguru\" \/><\/a><\/p>\n<p style=\"text-align: justify;\"><strong>Referensi:<\/strong><\/p>\n<p style=\"text-align: left;\">Sinaga, B., Sinambela, P., Sitanggang, A., dkk. (2017) Matematika. Jakarta: Kemendikbud.<\/p>\n<p style=\"text-align: left;\"><strong>Sumber Gambar:<\/strong><\/p>\n<p style=\"text-align: left;\">Gambar &#8216;Contoh Fungsi&#8217; [Daring]. Tautan: https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a5\/Bijection.svg\/250px-Bijection.svg.png (Diakses: 16 Februari 2022)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kamu sudah tahu belum apa yang dimaksud dengan fungsi komposisi? Kalau belum, yuk, kita pelajari bersama melalui artikel Matematika kelas 10 ini! Ada contoh soalnya juga, lho! &#8212; &nbsp; Kamu pasti sudah tidak asing dengan istilah fungsi, kan? Fungsi adalah relasi himpunan A ke himpunan B, dengan setiap anggota A dipasangkan ke tepat satu anggota [&hellip;]<\/p>\n","protected":false},"author":10,"featured_media":3529,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Fungsi%20Komposisi.png"],"_edit_last":["1"],"_edit_lock":["1753697239:1"],"_wp_old_date":["2022-02-18"],"_aioseo_title":["Belajar Fungsi Komposisi, Sifat &amp; Contohnya, Lengkap!"],"_aioseo_description":["Kamu sudah tahu belum apa yang dimaksud dengan fungsi komposisi? Kalau belum, yuk, kita pelajari bersama melalui artikel ini! 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