Domain of a function
In
mathematics, the
domain of a
function is the set of all input values to the function.
Given a function , the set A is called the domain, or domain of definition of f.
The set of all values in the codomain that f maps to is called the range of f, or f(A).
A well-defined function must map every element of the domain to an element of its codomain.
So, for example, the function:
-
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:
-
-
The domain of given function can be restricted to a
subset.
Suppose that , and .
Then the restriction of
g to
S is written:
-
See also
codomain,
range of a function,
injective function,
surjective function,
bijective function