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# Suppose is a function defined for all real , and suppose is invertible (that is, exists for all in the

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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?

Mar 17, 2019

$$f(x) \text{ being invertible means that if }f(x)=f(y) \text{ then }x=y\\ \text{so we are looking for points where }x^2 = x^4\\ \text{Can you determine for which values of }x, ~x^2 = x^4 ~?$$