If \(f\) is a differentiable function such that
\[
f(1)=8
\]
and
\[
f'(1)=\frac18.
\]
If \(f\) is invertible and \(g=f^{-1}\), then
Show Hint
Remember the inverse function derivative formula:
\[
(f^{-1})'(a)=\frac{1}{f'(f^{-1}(a))}.
\]
First find \(f^{-1}(a)\), then substitute into the derivative of the original function.