Answer:
[tex](f\circ g)(3)=-7[/tex]
Step-by-step explanation:
The given functions are;
[tex]f(x)=-2x+7[/tex]
and
[tex]g(x)=x^2-2[/tex]
We need to first of all find [tex](f\circ g)(x)[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x)=f(x^2-2)[/tex]
[tex](f\circ g)(x)=-2(x^2-2)+7[/tex]
[tex](f\circ g)(x)=-2x^2+4+7[/tex]
[tex](f\circ g)(x)=-2x^2+11[/tex]
We now plug in x=3
[tex](f\circ g)(3)=-2(3)^2+11[/tex]
[tex](f\circ g)(3)=-18+11[/tex]
[tex](f\circ g)(3)=-7[/tex]
