## 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.