Question

What is the domain of the function

Answer 1

Step 1:

The radical function

Domain is all possible values of .

Note that a negative value under the square root sign is not possible.

Set the expression under the square root sign greater than or equal to 0.

Solve the inequality

Step 2:

Solve the related equation

 

and

and

and

Solutions of the equation are .

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Step 3:

The solutions are separate the number line into three intervals.

Now test  sample values in each interval to determine whether values in the interval satisfy the inequality.

Test interval   - value        Inequality                        Conclusion

                    True

                           False

                                 True

Note that the original inequality contains a “ ≥ ” symbol, We include it into set of solutions at .

Solutions of the inequality is or .

Domain of is

Solution:

Domain set is .