Calculus · Hard problem

A machine's output is $f(x)=x^3-3x^2+5x$ for input $x$ (which is always increasing, since $f'(x)=3x^2-6x+5>0$ for all $x$). Let $g=f^{-1}$. Engineers want the output level $b$ at which $g'(b)=\dfrac12$. Find $b$.