Solution
= Solution
\b[False.] Take $A=\{0\}$ and $B=C=\{0,1\}$, with $f(0)=0$ and $g=\operatorname{id}_B$. Then $f$ is an <injection> and $g$ is a <surjection>, but the <function composition> $g\circ f$ has <image of a function> $\{0\}$, so it is not a <surjection> onto $C$.