Inverse

The notion of inverse in mathematical operation is simply the anti-operator. Note that it is different from reverse, where it can just be used to mean the order of presentation being reversed.

Excerpt from Wikipedia

The following paragraph is copied from Wikipedia.

Compositional inverseInverses and composition

If $f$ is an invertible function with domain $X$ and codomain $Y$, then

$f^{-1}\left(\,f(x)\,\right)=x$, for every $x\in X$; and $f\left(\,f^{-1}(y)\,\right)=y$, for every $y\in Y.$.

Using the composition of functions, we can rewrite this statement as follows:

$f^{-1}\circ f=\operatorname {id} _{X}$ and $f\circ f^{-1}=\operatorname {id} _{Y},$

where $\operatorname {id} _{X}$ is the identity function on the set $X$; that is, the function that leaves its argument unchanged. In Category Theory, this statement is used as the definition of an inverse morphism.

Related Pages

• Anti-operator