FINDING INVERSE OF A FUNCTION IS NOT ALWAYS EASY

Inverse functions look symmetric about x=y on the graph. So for finding $g'(1)$ what we can do is find (\f'(x)) at the point where it is equal to 1 and then take reciprocal of it. See it from the graph if it is hard to comprehend just by reading.

Now one solution that clearly strikes for $f(x)=1$ is x=0 and then we are done. Answer: $\boxed{2}$ Cheers

Since g(x) is inverse if f(x) g(f(x))=x

Diff wrt x g'(f(x))*f'(x)=1

Now f(0)=1 and f'(0)=.5 So g'(1)=1/f'(0)=2