Given:
[tex]g(x)=4x^2+3x-3[/tex]We're asked to find the value of:
[tex](g\circ g)(-1)[/tex]What we're going to do is to find the value of g(-1) first:
[tex](g\circ g)(-1)=g(g(-1))[/tex][tex]\begin{gathered} g(-1)=4(-1)^2+3(-1)-3 \\ g(-1)=4-3-3 \\ g(-1)=-2 \end{gathered}[/tex]Now,
[tex]g(g(-1))=g(-2)[/tex]The value of the composite function equals g(-2):
[tex]\begin{gathered} g(-2)=4(-2)^2+3(-2)-3 \\ g(-2)=4(4)-6-3 \\ g(-2)=16-6-3 \\ g(-2)=7 \end{gathered}[/tex]Therefore,
[tex](g\circ g)(-1)=7[/tex]