Diketahui f(x) = 2x + 3, g(x) = x2 - 3x - 4, dan h(x) = 3 - x, tentukan: a. (f o g)(x) b. (g o h)(x)

Diketahui f(x) = 2x + 3, g(x) = x² - 3x - 4, dan h(x) = 3 - x, tentukan:

a. (f o g)(x)

b. (g o h)(x)

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

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

Jawab:

a. (f o g)(x) = f(x² – 3x – 4)

= 2(x² – 3x – 4) + 3

= 2x² – 6x – 8 + 3

= 2x² – 6x – 5

b. (g o h)(x) = g(3 – x)

= (3 – x)² – 3(3 – x) – 4

= 9 – 6x + x² – 9 + 3x – 4

= x² – 3x – 4

c. ((f o g) o h)(x) = (f o g)(3 – x)

= 2(3 – x)² – 6(3 – x) – 5

= 2(9 – 6x + x²) – 18 + 6x – 5

= 18 – 12x + 2x² – 23 + 6x

= 2x² – 6x – 5

d. (f o (g o h))(x) = f(x² – 3x – 4)

= 2(x² – 3x – 4) + 3

= 2x² – 6x – 8 + 3

= 2x² – 6x – 5

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