Domain and Range

While defining real-valued functions, we have to observe some restriction. One such restriction is that we can never divide by zero (0). Hence in the function

,      cannot be equal to 1.

The set of values which  can take (so that the function is well defined) is known as the set of domain for that function.

Similarly the dependent variable y in the function, cannot take real values always. For example, in the function, the variable cannot take values which are greater than 1 or less than -1.

The set of values which can take is known as the Range of the Range for that function