Diketahui (f o g)(x) = 2x3 - 4x2 + 12x - 5. Tentukan: a. f(x) jika g(x) = x - 2 b. g(x) jika f(x) = 2x + 1

Diketahui (f o g)(x) = 2x³ - 4x² + 12x - 5. Tentukan:

a. f(x) jika g(x) = x - 2

b. g(x) jika f(x) = 2x + 1

Jawab:

(f o g)(x) = 2x³ – 4x² + 12x – 5

a. f(g(x)) = 2x³ – 4x² + 12x – 5

f(x – 2) = 2x³ – 4x² + 12x – 5

f((x – 2) + 2)) = 2(x + 2)³ – 4(x + 2)² + 12(x + 2) – 5

f(x) = 2(x³ + 6x² + 12x + 8) – 4(x² + 4x + 4) + 12x + 24 – 5

f(x) = 2x³ + 12x² + 24x + 16 – 4x² – 16x – 16 + 12x + 19

f(x) = 2x³ + 8x² + 20x + 19

b. f(g(x)) = 2x³ – 4x² + 12x – 5

2g(x) + 1 = 2x³ – 4x² + 12x – 5

2g(x) = 2x³ – 4x² + 12x – 5 – 1

g(x) = ½ (2x³ – 4x² + 12x – 6)

g(x) = x³ – 2x² + 6x – 3

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