The given functions are
[tex]\begin{gathered} f(x)=\frac{1}{x^2} \\ g(x)=e^x \end{gathered}[/tex]
To find g(f(x)) means substitute x in g by f
[tex]\begin{gathered} g(f(x))=e^{f(x)} \\ g(f(x))=e^{\frac{1}{x^2}} \end{gathered}[/tex]
To find f(g(0)) means replace x in f by g and substitute x by 0
[tex]\begin{gathered} f(g(x))=\frac{1}{(g(x))^2} \\ f(g(x))=\frac{1}{(e^x)^2} \\ f(g(x))=\frac{1}{e^{2x}} \end{gathered}[/tex]
Substitute x by 0
[tex]\begin{gathered} f(g(0))=\frac{1}{e^{2(0)}} \\ f(g(0))=\frac{1}{e^0} \\ e^0=1 \\ f(g(0))=\frac{1}{1} \\ f(g(0))=1 \end{gathered}[/tex]
