Answer: [tex]h(-2)=-1[/tex]
Step-by-step explanation:
We need to find [tex]f(g(x))[/tex]. Substitute the function [tex]g(x)[/tex] into the function [tex]f(x)[/tex]:
[tex]f(g(x)) = (x+ 2)^2- 1[/tex]
Now, we know that the function [tex]h(x)[/tex] is [tex]h(x)=f(g(x))[/tex], then:
[tex]h(x)=(x+ 2)^2- 1[/tex]
In order to find the value of [tex]h(-2)[/tex], we must substitute [tex]x=-2[/tex] into the function [tex]h(x)=(x+ 2)^2- 1[/tex].
Therefore, the value of [tex]h(-2)[/tex] is:
[tex]h(x)=(x+ 2)^2- 1\\\\h(-2)=(-2+ 2)^2- 1\\\\h(-2)=(0)^2- 1\\\\h(-2)=0-1\\\\h(-2)=-1[/tex]
