Given:
[tex]\begin{gathered} f(x)=x^2-6x-6 \\ \\ g(x)=-3x+11 \end{gathered}[/tex]
Find-: g(f(5))
So:
[tex]\begin{gathered} g(x)=-3x+11 \\ \\ g(f(x))=-3(x^2-6x-6)+11 \\ \\ g(f(x))=-3x^2+18x+18+11 \\ \\ g(f(x))=-3x^2+18x+29 \end{gathered}[/tex]
So the value of g(f(5))
[tex]\begin{gathered} g(f(x))=-3x^2+18x+29 \\ \\ g(f(5))=-3(5)^2+18(5)+29 \\ \\ g(f(5))=(-3\times25)+(18\times5)+29 \\ \\ g(f(5))=-75+90+29 \\ \\ g(f(5))=-75+119 \\ \\ g(f(5))=44 \end{gathered}[/tex]
So the value of g(f(5)) is 44
