Inverse of $f(x)=x^{0.2}+x^{0.5}$

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I have tried extensively to find the inverse of $f(x)=x^{0.2}+x^{0.5}$, but to no avail. I asked my algebra professor, and she didn't know either. I put the question into Wolfram Alpha, but it said "no results found in terms of standard mathematical functions". What is the inverse? Is it even possible?