Definition:Right Inverse Mapping

Definition
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 mapping such that:
 * $$f \circ g = I_T$$

where:
 * $$f \circ g$$ 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).

Also see

 * Surjection iff Right Inverse, which demonstrates that $$g$$ can not be defined unless $$f$$ is a surjection.