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:
[tex]h(-2)=1[/tex]
Substitute h(-2) into the expression f(h(-2)):
[tex]f(h(-2))=f(1)[/tex]
Substitute x=1 into the equation for the function f(x):
[tex]\begin{gathered} f(x)=x^2-4;x=1 \\ \Rightarrow f(1)=(1)^2-4=1-4=-3 \end{gathered}[/tex]
It follows that:
[tex]f(h(-2))=-3[/tex]
The answer is f(h(-2)) = -3.
