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Example:
Find domains and ranges of the following functions.
Solution:
(i) 
 Domain of  is 
i.e., 
Thus, the domain of ' ' is  .
 Range of  is non–negative values. As, 'x' varies over the domain of ' ' the corresponding 'y' values vary over the interval 
Thus, the Range of  is  .
(ii) 
For real values of ' '
 
Thus, the domain of  is  .
For the Range.
Thus, the range of  is  .
(iii) 
  is undefined if
Thus, the domain of  is all.
X except
 Range of is the set of real numbers.
i.e.  Example:
Find the range of the function .
Solution:
We have
Put
Thus, the domain is, 
Now for the range, we have
 
 
 
For 
So, the range of the function  is  . Example:
Let . Find the domain and range of  .
Solution:
We have
For , 
For 
Thus, the domain is .
Now for the Range, we have
 
 
 
 
 
For , 
Thus, the range of the function 
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