The reciprocal function of nonzero real numbers is a function that gives the multiplicative inverse of a number. That means, for any x, f(x)x = 1. It is defined for all real numbers excluding zero, which has no defined multiplicative inverse.

When it is extended to the entire set of real numbers by defining f(0) = 0, the reciprocal function extended within reals is obtained. It can also be extended to the set of extended real numbers by defining f(0) = ∞ and f(∞) = 0, giving the extended real-valued reciprocal function of extended real numbers.