A function is a rule that assigns to every element in a set \(D\) (domain) exactly one element in the set \(R\) (range).  We will treat functions as a set of ordered pairs \((x, y)\) where \(x\) is in the domain and \(y\) is in the range with \(y = f(x)\).

For example, if \(f(x)\) =\(\frac{3}{{(x + 15)}}\). The domain consists of all numbers for \(x\) that are defined for the function.  Since the function does not exist at  \(x = - 15\). Domain of the function is all real numbers excluding – 15.

Hence domain is the set of all the values of \(x\), for which function \(f(x)\) is defined. Suppose \(f(x)\) is \(\sqrt {x - 3} \), then \(f(x)\) is defined for all values of \(x\), except the values which are less than 3. Hence domain of the function is \(\left[ {3,{\rm{ }}\infty } \right)\). We can also write this domain in the form \(x \ge 3\).