Question

Given the definitions of f(x) and g(x) below, find the value of (fog)(-8).

f(x) = x2 – 3x – 12
g(x) = -x - 12

Answer 1

`(f \circ g)(-8) = 16`

Explanation:

The given function are;

f(x) = x² - 3·x - 12, and g(x) = -x - 12

`(f \circ g)(x) = f(g(x))`

Therefore;

`(f \circ g)(-8) = f(g(-8))`

g(-8) = -(-8) - 12 = 8 - 12 = -4

∴ f(g(-8)) = f(-4) = (-4)² - 3×(-4) - 12 = 16

Therefore;

`(f \circ g)(-8) = f(g(-8)) = 16`