# That's a great mapping

Calculus Level 4

Define a function $$f(x)$$ such that $$f(x)=x^{2}$$ for $$x \in [-1,1]$$ and $$f(x)=f(\frac{1}{x})$$ for all non-zero $$x$$.

Find $$\displaystyle \int_{-\infty}^{\infty} f(x)\, dx$$.

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