Inverse of a function

Revision as of 21:46, 4 March 2007 by JBL (talk | contribs) (TeX. Feh.)

The inverse of a function is a function that "undoes" the action of a given function.

For example, consider the function $f: \mathbb R \to R$ given by the rule $\displaystyle f(x) = x^2 + 6$. The function $g(x) = \sqrt{x-6}$ has the property that $f(g(x)) = x$. In this case, $g$ is called the (right) inverse function of $f$. (Similarly, a function $g$ such that $g(f(x))=x$ is called the left inverse function of $f$. Typically the right and left inverses coincide on a suitable domain, and in this case we simply call the right and left inverse function the inverse function. Often the inverse of a function $f$ is denoted by $f^{-1}$.

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