11I may be wrong, correct me if I'm so.
f(x)(x^3+x)=f(2x^2-1)
f(-12)=0
Consider
x=\frac{-1}{2}+\Delta x \\ \ \Delta x\rightarrow 0
f(\frac{-1}{2}+\Delta x)((\frac{-1}{2}+\Delta x)^3-\frac{1}{2}+\Delta x)=f(2x^2-1)
but since f(x) is continuous, lim_{\Delta x\rightarrow 0} (f(\frac{-1}{2}+\Delta x))\rightarrow 0
So we have f(2x2-1)=0
Thus f(x) turns out to be identically 0, and that seems to be the only function satisfying the given eqn!
