Need some hints to solve Ex6a from V. Zorich course of Analysis vol.1 chap.1 §3.
If mappings $f:X\to Y$ and $g:Y\to X$ are such that $g \circ f=id_X$ where $id_X$ - identity map X, then $g$ is called left inverse for $f$ and $f$ is called right inverse for g. Show that unlike the unique inverse map, there can exist many one-sided inverse maps.
Author's hint to regard set $X$, for example consisting of one element, set $Y$ of two elements.
using the fact that $g(f(x))=x$ and $f(g(y))=y$, then (may be) to use
lemma: $g \circ f=id_X => (g \quad surjective)\wedge(f\quad injective)$