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Noninvertible* FunctionsI've noticed that the inverse of f(x)=x^2 is NOT itself a function, but can still be described as f(-1)(x)=+/-sqrt(x). More or less, f(-1)(x)=sqrt(x)&-sqrt(x). Is there a name for situations like this, where the inverse of a function isn't a function itself but is a concatenation of functions? What about cases like the inverse of cosine, where the answer is more of an infinite family of answers than a single answer? |

Context dictates which solutions we take. |

In complex analysis there's a thing called a Riemann surface in which all the possible inverse values are taken as a single geometric structure. The Wiki article has some nice pictures of the Riemann surface for $\sqrt{z}$ and other familiar functions in which you can see what's going on. |

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