First, find the inverse of f,
[tex]y=e^x[/tex]
[tex]x=e^y[/tex]
Now take the natural logarithm on both sides,
[tex]\ln x=\ln e^y\implies f^{-1}(x)=\boxed{\ln(x)}[/tex]
Second, find the inverse of g,
[tex]y=5x\implies g^{-1}(x)=\boxed{\frac{x}{5}}[/tex]
Now take their composition,
[tex](g\circ f)(x)=g(f(x))=\frac{\ln(x)}{5}[/tex]
Let [tex]y=\frac{\ln(x)}{5}[/tex], now again find the inverse,
[tex]x=\frac{\ln(y)}{5}[/tex]
[tex]5x=\ln y[/tex]
exponentiate both sides to base e,
[tex]e^{5x}=e^{\ln y}\implies (g\circ f)^{-1}(x)=\boxed{e^{5x}}[/tex]
Hope this helps :)
