AMO · 2027 · Grades 8-9 · Self-study SET 22 Question 14

Let $f(x)=2^x+86$ and $g(x)=3x^2+x-4$. Find $g\bigl(f^{-1}(g(14))\bigr)$. Here $f^{-1}$ means the inverse function of $f$, not a reciprocal. Enter the numerical value.