<P> For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0 (ignoring complex numbers in both cases). </P> <P> If the domain of a function is a subset of the real numbers and the function is represented in a Cartesian coordinate system, then the domain is represented on the X-axis . </P> <P> Given a function f: X → Y (\ displaystyle f \ colon X \ to Y), the set X (\ displaystyle X) is the domain of f (\ displaystyle f); the set Y (\ displaystyle Y) is the codomain of f (\ displaystyle f). In the expression f (x) (\ displaystyle f (x)), x (\ displaystyle x) is the argument and f (x) (\ displaystyle f (x)) is the value . One can think of an argument as a member of the domain that is chosen as an "input" to the function, and the value as the "output" when the function is applied to that member of the domain . </P> <P> The image (sometimes called the range) of f (\ displaystyle f) is the set of all values assumed by f (\ displaystyle f) for all possible x (\ displaystyle x); this is the set (f (x) x ∈ X) (\ displaystyle \ left \ (f (x) x \ in X \ right \)). The image of f (\ displaystyle f) can be the same set as the codomain or it can be a proper subset of it . It is, in general, smaller than the codomain; it is the whole codomain if and only if f (\ displaystyle f) is a surjective function . </P>

The domain of f(x) = cos(x) is all real numbers