To find the domain of a function f, we use the fact that the domain is the set of all real

numbers x for which f(x) is a real number.

The range of a function f : A -> B is the set of all values taken by f i.e. it is the set of

images of elements in the domain of f i.e.

Range(f) = {f(x) | x ∈ A}

Let us take an example.

Example:  f(x) = 1/(x - 5)

1. Domain:

Given function is not defined when x - 5 = 0 i.e x = 5

So, Domain of f(x) = R - {5}   (R -> Real number) 

2. Range:

Let f(x) = y = 1/(x - 5)

=> x - 5 = 1/y

=> x = 5 + (1/y)

=> x = (5y + 1)/y

Here x is not defined when y = 0.

So, range of f(x) = R - {0}