Question

How do i use the graph and the equation to find the answer?

Answer 1

The equation of the function f(x) and the graph of h(x) are given. It is required to find use the graph and the equation to find f(h(-2)).

Notice from the graph of h(x) that the y-value corresponding to x=-2 is 1. This implies that:

`h(-2)=1`

Substitute h(-2) into the expression f(h(-2)):

`f(h(-2))=f(1)`

Substitute x=1 into the equation for the function f(x):

`\begin{gathered} f(x)=x^2-4;x=1 \\ \Rightarrow f(1)=(1)^2-4=1-4=-3 \end{gathered}`

It follows that:

`f(h(-2))=-3`

The answer is f(h(-2)) = -3.