1. The problem is to define a bijective function. 2. A function $f: A \to B$ is called \textbf{bijective} if it is both \textbf{injective} (one-to-one) and \textbf{surjective} (onto). 3. \textbf{Injective} means that for every $x_1, x_2 \in A$, if $f(x_1) = f(x_2)$ then $x_1 = x_2$. In other words, different inputs map to different outputs. 4. \textbf{Surjective} means that for every $y \in B$, there exists at least one $x \in A$ such that $f(x) = y$. This means the function covers the entire codomain. 5. Therefore, a bijective function pairs each element of $A$ with a unique element of $B$ and covers all elements of $B$. 6. An example of a bijective function is $f(x) = x + 1$ from the set of all integers $\mathbb{Z}$ to $\mathbb{Z}$. 7. This function is injective because if $f(x_1) = f(x_2)$ then $x_1 + 1 = x_2 + 1$ which implies $x_1 = x_2$. 8. It is surjective because for any integer $y$, choosing $x = y - 1$ gives $f(x) = y$. 9. Hence, $f$ is bijective.