Let us take an example.

Example:  f(x) = 1/(x-5)

1. Range:

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

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

2. Domain:

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}