Problem 403 (difficulty: 2/10)

Let \(\displaystyle f(x)=x^3\) if \(\displaystyle x\) is rational, and \(\displaystyle f(x)=-x^3\) if \(\displaystyle x\) is irrational. Does \(\displaystyle f(x)\) have a unique inverse on \(\displaystyle (-\infty,+\infty )\)?

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