if f(x) = ex and g(x) = log x show that fog=gof given x>0

Question

relations and functions: composition of functions class 12

Answer 1

f(x)=e^x; g(x)=log(x) (assume log(x) means ln(x)). Note that log(x) only exists for x>0.

f○g=f(g(x))=e^g(x)=e^log(x)=x;

g○f=g(f(x))=log(f(x))=log(e^x)=x=f○g.