In mathematics, an inverse function (or anti-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.
Example; Let F:R – be defined by f(x) = 2x + 1 show that f-1 is defined by f-1 = ½ (x -1)
Let f(x) = y,
then y = 2x + 1
Make x subject of formular
x = (y-1)/2
Therefore f-1 (x) = ½ (x-1).
The diagrammatic representative of an anti-function or inverse function is;
Generally we have;