## Encyclopedia > Domain (function)

Article Content

# Function domain

Redirected from Domain (function)

In mathematics, given a function fA → B, the set A is called the domain, or domain of definition of f.

A well-defined function must map every element of the domain to an element of its codomain. So, for example, the function:

f: x → 1/x

has no valid value for f(0). It is thus not a function on the set R of real numbers; R can't be its domain. It is usually either defined as a function on R \ {0}, or the "gap" is plugged by specifically defining f(0); for example:

f: x → 1/x , x ≠ 0
f: 0 → 0

The domain of given function can be restricted to a subset. Suppose that gA → B, and S ⊆ A. Then the restriction of g to S is written:

g|S: SB

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Las Cruces, New Mexico ... (608.2/mi²). The racial makeup of the city is 69.01% White, 2.34% African American, 1.74% Native American, 1.16% Asian, 0.07% Pacific Islander, 21.59% from oth ...