Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x^2)$ and $y=f(x^4)$ are drawn, at how many points do they intersect?

wassyo Jun 6, 2024

#1**+1 **

\(f(x) \text{ being invertible means that if }f(x)=f(y) \text{ then }x=y\\ \text{so we are looking for points where }x^2 = x^4\\ \)

There are 3 such points.

We have \(x=0, 1, -1\)

This means they intersect at 3 points.

I'm not sure if this is correct, though.

Thanks! :)

NotThatSmart Jun 6, 2024