The inverse element of an element

*x*from a set E for an operation ⊕ defined on E is the element*x*‘ of E such that*x*⊕*x*‘ =*n*where*n*∈ E is the identity element for the operation ⊕.### Examples

- The additive inverse of
*x*for addition in \(\mathbb{R}\) is the inverse element of*x*for this operation - The inverse of
*x*for multiplication in \(\mathbb{R}\) is the inverse element of*x*for this operation. - The reciprocal relationship \(f^{-1}\) of a function \(f\) defined in \(\mathbb{R}\) is the inverse element of \(f\) for the composition of functions, since \(f^{-1}\space ο\space f = I_{\mathbb{R}}\), where \( I_{\mathbb{R}}\) is the identity relation on \(\mathbb{R}\).