a. To find (fog)(x), evaluate f(x) at x=g(x), this is, replace each x in f(x) for g(x):
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=5(g(x))-1 \\ (f\circ g)(x)=5(\frac{x+1}{5})-1 \\ (f\circ g)(x)=x+1-1 \\ (f\circ g)(x)=x \end{gathered}[/tex]
b. Follow the same procedure for (gof)(x):
[tex]\begin{gathered} (g\circ f)(x)=g(f(x))=\frac{f(x)+1}{5} \\ (g\circ f)(x)=\frac{(5x-1)+1}{5} \\ (g\circ f)(x)=\frac{5x}{5} \\ (g\circ f)(x)=x \end{gathered}[/tex]
c. Evaluate the obtained expression at x=-1:
(fog)(x)=x
(fog)(-1)=-1
d. Evaluate the obtained expression at x=-1:
(gof)(x)=x
(gof)(-1)=-1
