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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?

 Jun 6, 2024
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\(f(x) \text{ being invertible means that if }f(x)=f(y) \text{ then }x=y\\ \text{so we are looking for points where }x^2 = x^4\\ \)

 

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! :)

 Jun 6, 2024

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