f(x) = e^x and g (x) = log_e x

Now, fog(x) = f(g(x)) = f(log_e x) = e^log_e^x= x

⇒ fog(x) = x

gof(x) = g(f(x)) = g(e^x) = log_e e^x = x

⇒ gof(x)=x

Hence, fog(x) = x and gof(x) = x