Find the Domain h(x) = square root of 6-x^2

Problem

h(x)=√(,6−x2)

Solution

1. Identify the condition for the square root function to be defined, which requires the radicand to be non-negative.

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 in interval notation to define the domain.

−√(,6)≤x≤√(,6)

Final Answer

Domain:[−√(,6),√(,6)]

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