Since g(x) is inverse of f(x), f(g(x)=x
Differentiating both sides w.r.t x, it would be
f'(g(x)) g'(x) =1
Thus for x=0, f'(g(0))g'(0)=1
The function is not invertible (it does not have an inverse).
We can use the result:
#g#is the inverse of #f#, then #g'(c) = 1/(f'(g(c))#
Therefore, if there were any such thing as an inverse of the function given, we would have