This question already has an answer here:
- Inverting a function in a certain region 3 answers
I want to calculate the inverse of
f[x_] := 1/2 - (x (4 x^2 - 9))/12 /; -1/2 <= x <= 1/2
f[x] is monotonic inside $-0.5 < x <= 0.5$, but I don't know how to calculate its inverse.