Given a function f: A → B, the set B is called the codomain of f. The codomain is not to be confused with the range f(A), which is in general only a subset of B.
Let the function f be a function on the real numbers:
Example
defined by
The codomain of f is R, but clearly f(x) never takes negative values, and thus the range is in fact the set R+ -- non-negative reals, ie the interval [0,∞):
- 0 ≤ f(x) < ∞
- g: R → R+
- g: x → x2
The codomain can affect whether or not the function is a surjection; in our example, g is a surjection while f is not.
See also: Function domain, Function range