Definition:Right Inverse Mapping

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Let $S, T$ be sets where $S \ne \varnothing$, i.e. $S$ is not empty.

Let $f: S \to T$ be a mapping.

Let $g: T \to S$ be a mapping such that:

$f \circ g = I_T$


$f \circ g$ denotes the composite mapping $g$ followed by $f$
$I_T$ is the identity mapping on $T$.

Then $g: T \to S$ is called a right inverse (mapping) of $f$.

Also see

In the context of abstract algebra:

from which it can be seen that a left inverse mapping can be considered as a left inverse element of an algebraic structure whose operation is composition of mappings.