1. Diketahui f(x)3x-5 dan g(x)=x+1. Tentukan (fog)(x) 2. Jika f(x)=x2+1 dan g(x)=x+1. Tentukan nilai (fog)(2) 3. Diketahui f(x)=x+3 dan fog (x)=x2+6x+7. Tentuka

1. Diketahui :

f(x)  = 3x - 5

g(x) = x + 1

Ditanya : (fog)(x) = ?

Dijawab :

(fog)(x) = f(g(x))

(fog)(x) = 3(x + 1) - 5

(fog)(x) = 3x + 3 - 5

(fog)(x) = 3x - 2

2. Diketahui :

f(x) = x² + 1

g(x) = x + 1

Ditanya : (fog)(2) = ?

Dijawab :

(fog)(x) = f(g(x))

(fog)(x) = (x + 1)² + 1

(fog)(x) = x² + 2x + 1 + 1

(fog)(x) = x² + 2x + 2

Lalu kita cari (fog)(2)

(fog)(x) = x² + 2x + 2

(fog)(2) = (2)² + 2(2) + 2

(fog)(2) = 4 + 4 + 2

(fog)(2) = 10

3. Diketahui :

f(x) = x + 3

(fog)(x) = x² + 6x + 7

Ditanya : g(x) = ?

Dijawab :

(fog)(x) = f(g(x))

x² + 6x + 7 = (g(x)) + 3

g(x) = x² + 6x + 7 - 3

g(x) = x² + 6x +4

4. Diketahui :

f(x) = 4x - 3

(foh)(x) = 5 + 4x - 20x²

Ditanya : h(-4) = ?

(foh)(x) = f(h(x))

5 + 4x - 20x² = 4(h(x)) - 3

4(h(x)) = 5 + 3 + 4x - 20x²

4(h(x)) = 8 + 4x - 20x²

h(x) = (8 + 4x - 20x²) ÷ 4

h(x) = 2 + x - 5x²

h(-4) = 2 + (-4) - 5(-4)²

h(-4) = 2 - 4 - 80

h(-4) = -82

5. Diketahui :

f(x) = 3x² - 4x + 6

g(x) = 2x - 1

(fog)(x) = 101

Ditanya : Nilai x yang memenuhi ?

Dijawab :

(fog)(x) = f(g(x))

(fog)(x) = 3(2x - 1)² - 4(2x - 1) + 6

(fog)(x) = 3(4x² - 4x + 1) - 8x + 4 + 6

(fog)(x) = 12x² - 12x + 3 - 8x + 10

(fog)(x) = 12x² - 20x + 13

Selanjutnya kita cari nilai x yang memenuhi

(fog)(x) = 101

12x² - 20x + 13 = 101

12x² - 20x + 13 - 101 = 0

12x² - 20x - 88 = 0

3x² - 5x - 22 = 0

(3x - 11)(x + 2) = 0

3x - 11 = 0

3x = 11

x1 = [tex]\frac{11}{3}[/tex]

x + 2 = 0

x = -2

∴ Maka nilai x yang memenuhi (fog)(x) = 101 adalah [tex]\frac{11}{3}[/tex] dan -2

Pelajari lebih lanjut :

1. https://brainly.co.id/tugas/29701335

2. https://brainly.co.id/tugas/27670624

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Detail Jawaban :

Kelas : X

Mapel : Matematika

Bab : Bab 3 - Fungsi Komposisi

Kode Kategorisasi : 10.2.3

Kata kunci : fungsi, fungsi komposisi