I want to find functions that are their own inverse function, so that
$$f(x) = f^{-1}(x)$$
and
$$f(f(x)) = x$$
I have managed to find the following examples:
$$f(x) = x$$
$$f(x) = -x + n$$
$$f(x) = \frac{1}{x - n} + n$$
Are there more examples?
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There are infinitely many examples, as you can take any graph that starts on the line $x=y$ and never crosses the line, and mirror the graph to the other side – 5xum May 18 '17 at 12:54
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Do you want continuous functions? What about the domain? Technically the function $f : {c} \to {c }$ given by $f(c) = c$ is its own inverse for all $c$. – May 18 '17 at 12:54
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2$f(x) = \sqrt[n]{a-x^n}$ – florence May 18 '17 at 13:00
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@5xum Why should such a thing be a function? – John Gowers May 18 '17 at 15:56