A step by step detailed worked examples of Domain and Range of a Function. Problems with detailed solutions on finding domain and range of functions were provided below. Before proceeding on worked examples check our previous post what is domain and what is range of a function? Steps to solve domain and range of a function.


Worked examples: Domain of a function 


  • Generally in question they do provided data whether x is less/greater/equal to the supplied number. But if they do no mention data then we will assume x as negative.
  • Next, Since the number is under root therefore (2 - x) would be greater equal to zero, i.e., 2-x is greater equal to 0. which yields x less equal to 2.


  • Same trick as of Q.1 is applied in this problem.  After doing some simple calculations on last line it will be found that x is greater  than both 1 and 8. So the domain of the function is bounded in between [1,8] .
Check more solved examples on domain of a function

 Worked examples: Range of a function

In this question data is supplied that x (never equals to 3) [clearly we can cancel out (3-x) and (x-3) which will yield -1 as result. So, its range is {-1}.

  • For solving problems like of above at first the numerator and denominator have to be simplified to its simplest form. 
  • After that we have to find value(solution) of "y".
  • Obviously in step ii we got 2 values of y, if  done correctly in step 2, taking those value we will represent range of the function.