Find the Domain square root of 6-x^2

Problem

√(,6−x2)

Solution

1. Identify the condition for the square root function to be defined. The expression inside the square root (the radicand) must be greater than or equal to zero.

6−x2≥0

2. Rearrange the inequality to isolate the variable term.

−x2≥−6

3. Multiply both sides by −1 and reverse the inequality sign.

x2≤6

4. Solve the quadratic inequality by taking the square root of both sides.

|x|≤√(,6)

5. Express the solution as a compound inequality.

−√(,6)≤x≤√(,6)

6. Write the domain in interval notation.

[−√(,6),√(,6)]

Final Answer

Domain=[−√(,6),√(,6)]

Want more problems? Check here!