Diketahui f(x) = x + 2, g(x) = 3x - 1, dan h(x) = x² + 2x - 5. Tentukan: a. (h o g o f)(x) b. (g o h o f)(x)

Diketahui f(x) = x + 2, g(x) = 3x - 1, dan h(x) = x² + 2x - 5. Tentukan:

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

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

Jawab:

f(x) = x + 2

g(x) = 3x – 1

h(x) = x² + 2x – 5

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

= h(g(f(x)))

= h(g(x + 2))

= h(3(x + 2) – 1)

= h(3x + 6 – 1)

= h(3x + 5)

= (3x + 5)² + 2(3x + 5) – 5

= 9x² + 30x + 25 + 6x + 10 – 5

= 9x² + 36x + 30

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

= g(h(f(x)))

= g(h(x + 2))

= g((x + 2)² + 2(x + 2) – 5)

= g(x² + 4x + 4 + 2x + 4 – 5)

= g(x² + 6x + 3)

= 3(x² + 6x + 3) – 1

= 9x² + 18x + 9 – 1

= 9x² + 18x + 8

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