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

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 Mar 17, 2019
edited by Rom  Mar 17, 2019

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