Diketahui f(x) = x2 + 4x - 5, g(x) = x + 2, dan h(x) = 1 - x. Tentukan nilai x Jika: a. (f o g o h)(x) = -5 b. (g o f o h)(x) = 9

Diketahui f(x) = x² + 4x - 5, g(x) = x + 2, dan h(x) = 1 - x. Tentukan nilai x Jika:

a. (f o g o h)(x) = -5

b. (g o f o h)(x) = 9

Jawab:

a. (f o g o h)(x) = -5

⇔ f(g(h(x))) = -5

⇔ f(g(1 – x)) = -5

⇔ f(1 – x + 2) = -5

⇔ f(3 – x) = -5

⇔ (3 – x)² + 4(3 – x) – 5 = -5

⇔ x² – 6x + 9 + 12 – 4x – 5 + 5 = 0

⇔ x² – 10x + 21 = 0

⇔ (x – 3)(x – 7) = 0

⇔ x = 3 atau x = 7

b. (g o f o h)(x) = 9

⇔ g(f(h(x))) = 9

⇔ g(f(1 – x)) = 9

⇔ g((1 – x)² + 4(1 – x) – 5) = 9

⇔ g(x² – 2x + 1 + 4 – 4x – 5) = 9

⇔ g(x² – 6x) = 9

⇔ x² – 6x + 2 = 9

⇔ x² – 6x – 7 = 0

⇔ (x + 1)(x – 7) = 0

⇔ x = -1 atau x = 7

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