Diketahui fungsi f(x) = x2 + 7x – 4 dan g(x) = 2x

Diketahui fungsi f(x) = x2 + 7x – 4 dan g(x) = 2x – 5. Tentukan:

Diketahui fungsi f(x) = x²+ 7x – 4 dan g(x) = 2x – 5. Tentukan:

a. (f o g) (x)

b. (g o f) (x)

c. (f o g) (3)

d. nilai a jika (g o f) (a) = -25

Jawab:

a. (f o g) (x) = f(g(x))

= f(2x – 5)

= (2x – 5)² + 7(2x – 5) – 4

= 4x² – 20x + 25 + 14x – 35 – 4

= 4x² – 6x – 14

b. (g o f) (x) = g(fx)

= g(x²+ 7x – 4)

= 2(x²+ 7x – 4) – 5

= 2x²+ 14x – 8 – 5

= 2x²+ 14x – 13

c. (f o g) (3)

= 4(3)² – 6 . 3 – 14

= 36 – 18 – 14

= 4

d. (g o f) (a) = -25

2a²+ 14a – 13 = -25

2a²+ 14a + 12 = 0

a² + 7a + 6 = 0

(a + 6) (a + 1) = 0

a = -6 atau a = -1

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