Codomain of a Function

• Definition: The set that contains all possible outputs of the function $f:A\to B$.
• Note: the codomain is chosen when defining the function. Not every element of the codomain must be “hit” by the function.
• Note: any superset of a function’s image is a valid codomain for that function.
• Example: For $f(X)=x^2$ defined as $f:\mathbb{R}\to \mathbb{R}$, the codomain if $\mathbb{R}$.