Question

f(x) = x+5 g(x) = -x^2 - 5x Find f(g(-4))

Answer 1

Given data:

The first function given is f(x)=x+5.

The second function given is g(x)=-x^2-5x.

The expression for f(g(x)) is,

$\begin{gathered} f(g(x))=f(-x^2-5x) \\ \text{ =-x}^2-5x+5 \end{gathered}$

Substitute -4 for x in the above expression.

$\begin{gathered} f(g(-4))=-(-4)^2-5(-4)+5 \\ =-16+20+5 \\ =9 \end{gathered}$

Thus, the value of f(g(-4)) is 9.