If the operation * is associative then if an element has both a left inverse and a right inverse, they are equal.
12.
In these cases it can happen that; then " inverse " typically implies that an element is both a left and right inverse.
13.
A function has a right inverse if and only if it is surjective ( though constructing such an inverse in general requires the axiom of choice ).
14.
It follows that the identity element, " e ", is unique, and that every element of " Q " has a unique right inverse.
15.
However, if is a left inverse for, then may or may not be a right inverse for; and if is a right inverse for, then is not necessarily a left inverse for.
16.
However, if is a left inverse for, then may or may not be a right inverse for; and if is a right inverse for, then is not necessarily a left inverse for.
17.
This is generally justified because in most applications ( e . g . all examples in this article ) associativity holds, which makes this notion a generalization of the left / right inverse relative to an identity.
18.
To be a branch of an inverse function, g ( z ) must be a right inverse of f ( z ) ( where f ( z ) = z 3 ), and it must be continuous.
19.
The transfer function can be used to define an operator F [ r ] = u that serves as a right inverse of " L ", meaning that L [ F [ r ] ] = r.
20.
:To figure that out, look at some diagrams like the ones at inverse function and keep in mind the definition of a right inverse . & mdash; Carl ( talk ) 11 : 46, 7 May 2009 ( UTC)
