Question

Given the definitions of f(x) and g(x) below, find the value of (gºf)(-4).

f(x) = -2x - 3
g(x) = 2x2 – 2x – 8

Answer 1

`(g\circ f)(-4) = 32`

Explanation:

We are given the two functions:

`f(x) = -2x - 3\text{ and } g(x) = 2x^2 - 2x - 8`

And we want to find the value of:

`(g\circ f)(-4)`

Recall that this is equivalent to:

`\displaystyle = g(f(-4))`

Find f(-4):

`\displaystyle \begin{aligned}f(-4) &= -2(-4) - 3 \\ &= 5 \end{aligned}`

Hence:

`g(f(-4)) = g(5)`

Finally, find g(5):

`\displaystyle \begin{aligned}g(5)& = 2(5)^2 - 2(5) - 8 \\ &= 32 \end{aligned}`

In conclusion:

`(g\circ f)(-4) = 32`