f and g are two differentiable functions which satisfy the condition g'a=2,g(a)=b and (fog)=I identify function,then f'(b) is equal to

Hi,

Identity function  i.e.    f [g(x)]= x

 differentiate both sides we get    f '[ g(x) ] g '(X) =1

              Put x=a  we get               f '(b).2=1

                                                        f '(b)=1/2