A function $f: A \to B$ is INJECTIVE (one-to-one) if

1. INJECTIVE (one-to-one): $f(x_1) = f(x_2)$ IMPLIES $x_1 = x_2$. Equivalently: distinct inputs → distinct outputs. 2. SURJECTIVE (onto): every $b \in B$ has some preimage $a \in A$ with $f(a) = b$. 3. BIJECTIVE: both injective AND surjective. 4. Examples on $f: \mathbb{R} \to \mathbb{R}$: - $f(x) = x^2$ is NEITHER (not injective: $f(1)=f(-1)$; not surjective: $-1$ has no preimage) - $f(x) = 2x$ is BIJECTIVE 5. Option A defines surjective. Options C, D are unrelated. _Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §0.5 (Functions — types)._