Diketahui :
[tex]\bf{f\left(x\right)=5x+2}[/tex]
[tex]\bf{g\left(x\right)=2x^{2}-6x-8}[/tex]
Maka
[tex]\boxed{\bf{\left(f+g\right)\left(x\right)=2x^{2}-x-6}}[/tex]
[tex]\boxed{\bf{\left(f-g\right)\left(x\right)=-\left(2x^{2}-11x-10\right)}}[/tex]
[tex]\boxed{\bf{\left(f\times g\right)\left(x\right)=2\left(5x^{3}+2x^{2}-21x-28\right)}}[/tex]
[tex]\boxed{\bf{\left(f:g\right)\left(x\right)=\frac{\left(5x+2\right)}{\left(2x^{2}-6x-8\right)}}}[/tex]
[tex] \: [/tex]
Fungsi KomposisiPendahuluan A. Definisi Fungsi
Fungsi dari himpunan A ke Himpunan B => relasi yang memetakan setiap anggota A dengan tetap satu anggota B.
[tex] \: [/tex]
[tex] \small\boxed{\boxed{\mathbf{B.\ \ Domain,\ Kodomain,\ dan\ Range}}}[/tex]
Suatu fungsi f memetakan A ke B (f : A → B) dan jika x ∈ A dan y ∈ B, maka f : x → y atau f(x) = y, sehingga :
[tex] \tiny\boxed{\begin{array}{c}\mathbf{1. \ domain\ (daerah\ asal)}\\\mathbf{\to himpunan\ semua\ anggota\ A\ dari\ pasangan\ terurut \ (x,y)}\\\\\mathbf{2.\ Kodomain\ \left(daerah\ kawan\right)}\\\mathbf{\to himpunan\ semua\ anggota\ himpunan\ B.}\\\\\mathbf{3.\ Range\ \left(daerah\ hasil\right)}\\\mathbf{\to himpunan\ semua\ anggota\ himpunan\ B\ dari\ pasangan\ terurut \ (x,y).}\end{array}}[/tex]
[tex] \: [/tex]
[tex] \boxed{\boxed{\mathbf{C.\ \ Operasi\ Aljabar}}}[/tex]
[tex] \scriptsize\boxed{\begin{array}{c}\mathbf{1.\ Penjumlahan\ dan\ Pengurangan\ Fungsi}\\\mathbf{\left(f\pm g\right)\left(x\right)=f\left(x\right)\pm g\left(x\right)}\\\\\mathbf{2.\ Perkalian\ Fungsi}\\\mathbf{\left(f\ .\ g\right)\left(x\right)=f\left(x\right)g\left(x\right)}\\\\\mathbf{3.\ Pembagian\ Fungsi}\\\mathbf{\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}}\\\\\mathbf{4.\ Perpangkatan}\\\mathbf{\left(f\left(x\right)\right)^{n}=f^{n}\left(x\right)}\end{array}}[/tex]
[tex] \: [/tex]
[tex] \boxed{\boxed{\mathbf{D,\ \ Fungsi\ Komposisi}}}[/tex]
[tex] \scriptsize\mathbf{1.\ Fungsi\ komposisi\ dapat\ ditulis\ sebagai\ :}\\\\\mathbf{\left(f \circ g\right)\left(x\right)=f\left(g\left(x\right)\right)\to komposisi\ g}\\\mathbf{\left(g \circ f\right)\left(x\right)=g\left(f\left(x\right)\right)\to komposisi\ f}[/tex]
[tex] \boxed{\underbrace{\mathbf{x\to_{g}\ g\left(x\right)\to_{f}\ f\left(g\left(x\right)\right)}}_{\mathbf{\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)}}} [/tex]
[tex] \: [/tex]
[tex] \: [/tex]
Pembahasan
Diketahui :
[tex]\bf{f\left(x\right)=5x+2}[/tex]
[tex]\bf{g\left(x\right)=2x^{2}-6x-8}[/tex]
Ditanya :
[tex]\bf{A.\ \left(f+g\right)\left(x\right)=...?}[/tex]
[tex]\bf{B.\ \ \left(f-g\right)\left(x\right)=...?}[/tex]
[tex]\bf{C.\ \ \left(f\times g\right)\left(x\right)=...?}[/tex]
[tex]\bf{D.\ \ \left(f:g\right)\left(x\right)=...?}[/tex]
Jawaban :
[tex]\bf{A.\ \left(f+g\right)\left(x\right)=...?}[/tex]
[tex]\bf{\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)}[/tex]
[tex]\bf{\left(f+g\right)\left(x\right)=\left(5x+2\right)+\left(2x^{2}-6x-8\right)}[/tex]
[tex]\boxed{\bf{\left(f+g\right)\left(x\right)=2x^{2}-x-6}}[/tex]
↔↔↔↔↔↔↔↔↔↔↔↔↔
[tex]\bf{B.\ \ \left(f-g\right)\left(x\right)=...?}[/tex]
[tex]\bf{\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right)}[/tex]
[tex]\bf{\left(f-g\right)\left(x\right)=\left(5x+2\right)-\left(2x^{2}-6x-8\right)}[/tex]
[tex]\bf{\left(f-g\right)\left(x\right)=-2x^{2}+11x+10}[/tex]
[tex]\boxed{\bf{\left(f-g\right)\left(x\right)=-\left(2x^{2}-11x-10\right)}}[/tex]
↔↔↔↔↔↔↔↔↔↔↔↔↔
[tex]\bf{C.\ \ \left(f\times g\right)\left(x\right)=...?}[/tex]
[tex]\bf{\left(f\times g\right)\left(x\right)=f\left(x\right)\times g\left(x\right)}[/tex]
[tex]\bf{\left(f\times g\right)\left(x\right)=\left(5x+2\right)\times\left(2x^{2}-6x-8\right)}[/tex]
[tex]\bf{\left(f\times g\right)\left(x\right)=10x^{3}-30x-40+4x^{2}-12x-16}[/tex]
[tex]\bf{\left(f\times g\right)\left(x\right)=10x^{3}+4x^{2}-42x-56}[/tex]
[tex]\boxed{\bf{\left(f\times g\right)\left(x\right)=2\left(5x^{3}+2x^{2}-21x-28\right)}}[/tex]
↔↔↔↔↔↔↔↔↔↔↔↔↔
[tex]\bf{D.\ \ \left(f:g\right)\left(x\right)=...?}[/tex]
[tex]\bf{\left(f:g\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}}[/tex]
[tex]\boxed{\bf{\left(f:g\right)\left(x\right)=\frac{\left(5x+2\right)}{\left(2x^{2}-6x-8\right)}}}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
Pelajari Lebih Lanjut :
- Contoh soal mencari fungsi komposisi -> (g o f) (x) : https://brainly.co.id/tugas/49941623
- Contoh soal fungsi komposisi -> (f o g) (x) : https://brainly.co.id/tugas/49193757
- Contoh soal Diketahuai f o g(x) = 6x² + 7 dan g(x) = 3x²+ 4, tentukan fungsi f (x) : https://brainly.co.id/tugas/50087120
- Contoh soal Jika f(x) =x²-x dan g(x) =1-2x ,maka a. f(x) + g(x) dan b. f(x) - g(x) : https://brainly.co.id/tugas/50195884
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Detail Jawaban
Kelas : 11 SMA
Bab : 2
Sub Bab : Bab 6 - Fungsi
Kode Kategorisasi : 11.2.6
Kata Kunci : Fungsi Komposisi.
