B. Jawablah pertanyaan-pertanyaan berikut dengan tepat! 1. Diketahui fungsi f(x) = 3x – 5 dan g(x) = 2x + 1. Tentukan: a. (fºg)(x) c. (g• f(x) b. (fog)(2) d. (gof)(6)
komposisi fungsi
–
f (x) = 3x – 5
g (x) = 2x + 1
(f o g)(x) = f (g(x))
(f o g)(x) = 3(2x + 1) – 5
(f o g)(x) = 6x + 3 – 5
(f o g)(x) = 6x – 2
(g o f)(x) = g (f(x))
(g o f)(x) = 2(3x – 5) + 1
(g o f)(x) = 6x – 10 + 1
(g o f)(x) = 6x – 9
(f o g)(x) = 6x – 2
(f o g)(2) = 6(2) – 2
(f o g)(2) = 10
(g o f)(x) = 6x – 9
(g o f)(6) = 6(6) – 9
(g o f)(6) = 27
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Penjelasan dengan langkah-langkah:
>>> Bagian A <<<
- (f o g)(x) = f {g(x)}
- (f o g)(x) = f (2x + 1)
- (f o g)(x) = 3(2x + 1) – 5
- (f o g)(x) = 6x + 3 – 5
- (f o g)(x) = 6x – 2
>>> Bagian B <<<
- (f o g)(x) = 6x – 2
- (f o g)(2) = 6(2) – 2
- (f o g)(2) = 12 – 2
- (f o g)(2) = 10
>>> Bagian C <<<
- (g o f)(x) = g {f(x)}
- (g o f)(x) = g (3x – 5)
- (g o f)(x) = 2(3x – 5) + 1
- (g o f)(x) = 6x – 10 + 1
- (g o f)(x) = 6x – 9
>>> Bagian D <<<
- (g o f)(x) = 6x – 9
- (g o f)(6) = 6(6) – 9
- (g o f)(6) = 36 – 9
- (g o f)(6) = 27