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) ​

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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

____

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

♦ Si Hebat