= Solution
The <image of a function> $f:A\to B$ is
$$
\boxed{f(A)=\{f(a):a\in A\}\subseteq B.}
$$
The <function> is <surjective>, or onto, exactly when every $b\in B$ equals $f(a)$ for at least one $a\in A$, equivalently $f(A)=B$. It is <injective>, or one-to-one, exactly when
$$
\boxed{\forall a,a'\in A,\quad f(a)=f(a')\Longrightarrow a=a'.}
$$
Thus <surjectivity> concerns whether the entire <codomain> is reached; <injectivity> concerns whether distinct inputs have distinct outputs.
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