Inverse function
In mathematics, an
inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa. i.e.,
f(
x) =
y if and only if
g(
y) =
x. A function f that has an inverse is said to be
invertible. When it exists, the inverse function is uniquely determined by f and is denoted by
f −1, read
f inverse. Superscripted "−1" does not, in general, refer to numerical exponentiation. In some situations, for instance when f is an invertible real-valued function of a real variable, the relationship between f and
f−1 can be written more compactly, in this case,
f−1(
f(
x)) =
x =
f(
f−1(
x)), meaning
f−1 composed with f, in either order, is the identity function on
R.