Inverse function with two $x$'s

Question

In the case of the function $f(x)=x^2+x^4$ is there any trick to inversing it? as the only ways I know do not work on it. As you cannot make y the subject through rearranging it.

Thanks in advance.

Answer 1

Setting $$y=x^2+x^4$$ we get $$x^4+x^2-y=0$$ solving this using the quadratic formula we obtain $$x^2_{1,2}=-\frac{1}{2}\pm\sqrt{\frac{1}{4}+y}$$ can you go on?