Given the functions below
[tex]\begin{gathered} f(x)=x^2-2 \\ g(x)=9-x \end{gathered}[/tex]
We are to find (fg)(-x)
SOLUTION
First of all, we have to get (fg)(x)
[tex](fg)(x)=(x^2-2)(9-x)[/tex]
Expand the function
[tex]\begin{gathered} (fg)(x)=x^2(9-x)-2(9-x) \\ (fg)(x)=9x^2-x^3-18+2x \\ \therefore(fg)(x)=-x^3+9x^2+2x-18 \end{gathered}[/tex]
Let us now solve for (fg)(-7)
[tex]\begin{gathered} (fg)(-7)=-(-7)^3+9(-7)^2+2(-7)-18 \\ (fg)(-7)=343+441-14-18=752 \end{gathered}[/tex]
Hence,
[tex](fg)(-7)=752[/tex]
