Let $f:[0,1] \to [0,2]$ be given by $f(x)=x^2+x^4$. Determine if f is an invertible function. If it is, compute its inverse. If it is not invertible, provide an argument to support your claim.
I think that $f$ is invertible because the restrictions on the domain and codomain make it bijective, but I am struggling to compute the inverse. Usually, if I was given $y=f(x)$ I would just rearrange to make x the subject and then swap $x$ and $y$, but I don't know how to do that for this example. Any help would be greatly appreciated.