However, more than one value of x can give the same output f(x). For example, if g is the function defined by g(x) = x2 − 2x + 3 then and g(0) = 3 and g(2) = 3.This video shows some examples of functions defined by equations.
The domain of a function is the set of all permissible inputs, that is, all permissible values of the variable x. For the functions f and g defined above, the domain is the set of all real numbers.
Sometimes the domain of the function is given explicitly and is restricted to a specific set of values of x. For example, we can define the function h by h(x) = x2 + 2 for −3 ≤ x ≤ 3. Without an explicit restriction, the domain is assumed to be the set of all values of x for which f(x) is a real number.
The following videos show how to find the domain of a function.
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