Let be a function from R into R. Determine the range of f.

Given:  

     
To Find:         

Range of any function is the set of values obtained after mapping is done in domain of the function

So every value of the co domain that are being mapped is Range of the function

For finding the range of any function 

Let y = f(x)

and then find the values of y for which x exists.


 

Now, 1 - y should be greater than zero and y should be greater than and equal to zero for x to exist because other than those values the x will be imaginary


Thus, 

1 - y > 0 
 
y < 1

and, y ≥ 0

Hence,

0 ≤ y < 1 will be the range of f(x)