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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
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Answer:
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Answer 1

The value of
`f\,\circ\,g(-8)` is 16.

Explanation:

The composition consist: in replacing the independent variable (
`x`) of
`f(x)` by
`g(x)`:

`f(x) = x^(2)-3\cdot x -12` (1)

`g(x) = -x-12` (2)

`f\,\circ\,g (x) = (-x-12)^(2) - 3\cdot (-x-12) -12` (3)

`f\,\circ\,g(x) = (x^(2)+24\cdot x + 144) +(3\cdot x +36) - 12`

`f\,\circ\,g(x) = x^(2) +27\cdot x +168`

`f\,\circ g(-8) = (-8)^(2)+27\cdot (-8) +168`

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

The value of
`f\,\circ\,g(-8)` is 16.