AMO 2027 Grades 9-11 SET 2 - Self-study Question 10

If $f(x)=2^x+86$ and $g(x)=3x^2+x-4$, find $$g\!\left[f^{-1}(g(14))\right].$$ Here $f^{-1}$ denotes the inverse function, not the reciprocal of $f$.



Enter one positive integer, without units.