1. The problem statement, all variables and given/known data The problem is to prove that: if f(g(x))=x ........... (1) and g(f(x))=x ............(2) then f(x)=g-1(x) 3. The attempt at a solution Differentiating (1) wrt x f'(g(x))*g'(x)=1 f'(g(x))=1/g'(x) As the slopes are reciprocals of each other, hence f(x)=g-1(x) Is this as simple as it seems? Are there any possible exceptions? Is there any more explanatory proof???? Please help me.