Diketahui f(x) = x + 1, g(x) = 2x - 3, dan h(x) = x2 + 3x - 2. Tentukan: a. (h o g o f)(x) b. (g o h o f)(x)

Diketahui f(x) = x + 1, g(x) = 2x - 3, dan h(x) = x² + 3x - 2. Tentukan:

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

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

Jawab:

f(x) = x + 1

g(x) = 2x – 3

h(x) = x² + 3x – 2

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

= h(g(f(x)))

= h(g(x + 1))

= h(2(x + 1) – 3)

= h(2x – 1)

= (2x – 1)² + 3(2x – 1) – 2

= 4x² – 4x + 1 + 6x – 3 – 2

= 4x² + 2x – 4

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

= g(h(f(x)))

= g(h(x + 1))

= g((x + 1)² + 3(x + 1) – 2)

= g(x² + 2x + 1 + 3x + 3 – 2)

= g(x² + 5x + 2)

= 2(x² + 5x + 2) – 3

= 2x² + 10x + 1

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