Calculus (3rd Edition)

$$\frac{1}{12}.$$
Since $g(x)$ is the inverse of $f(x)$, then $g(8)=g(f(-1))=-1$ and hence $$g'(x)=\frac{1}{f'(g(x))}\Longrightarrow g'(8)=\frac{1}{f'(-1)}=\frac{1}{12}.$$