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- Jan 26, 2012

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I don't know what to title this but will change it if $f(f(x))$ has a name. Anyway, I need to find $f(x)$ such that $f(f(x))=-x$. My friend gave me this challenge question and I haven't been able to figure it out.

There are many examples where $f(f(x))=x$ for example \(\displaystyle f(x)=\frac{1}{x}\) but that doesn't work for this one. I also tried a piecewise function but that didn't work either.

Lastly $f: \mathbb{R} \rightarrow \mathbb{R}$

Any ideas?

There are many examples where $f(f(x))=x$ for example \(\displaystyle f(x)=\frac{1}{x}\) but that doesn't work for this one. I also tried a piecewise function but that didn't work either.

Lastly $f: \mathbb{R} \rightarrow \mathbb{R}$

Any ideas?

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