Answer::
[tex]g\mleft(f\mleft(x\mright)\mright)=-5x^2+5x-78[/tex]Explanation:
Given the polynomials f(x) and g(x) defined below:
[tex]\begin{gathered} f\mleft(x\mright)=x^2-x+14 \\ g\mleft(x\mright)=-5x-8 \end{gathered}[/tex]The composite function: g(f(x))
[tex]\begin{gathered} g\mleft(f\mleft(x\mright)\mright)=-5(f(x))-8 \\ =-5(x^2-x+14)-8 \\ =-5x^2+5x-70-8 \end{gathered}[/tex]Therefore:
[tex]g\mleft(f\mleft(x\mright)\mright)=-5x^2+5x-78[/tex]