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

Answer:

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

Step-by-step 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:

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