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1.4 Inverse Functions

Inverse Functions

Inverse function - Wikipedia
  • A function maps the domain to the range. An inverse function simply does the opposite.
  • However, recall that a function must have the type of relation which is a one-to-one relation. Therefore, if the inverse function (which, yes, is a function) exists, the inverse must have a one-to-one relation too.
  • This implies that for an inverse function to exist (might be over a certain subset of the domain), the function must be one-to-one (over that particular subset if applicable).
  • We denote the inverse of f as f^{-1}. In particular, if f(x)=y, then f^{-1}(y)=x.
  • Therefore, we can deduce that:
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