Find the Domain g(x) = sixth root of 3-x

Problem

g(x)=√(6,3−x)

Solution

1. Identify the restriction for an even root. For any function ƒ(x)=√(n,u(x)) where n is an even integer, the radicand u(x) must be greater than or equal to zero to remain in the set of real numbers.

2. Set up the inequality based on the radicand.

3−x≥0

3. Solve the inequality for x by subtracting 3 from both sides.

−x≥−3

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

x≤3

5. Express the domain in interval notation. Since x can be any value less than or equal to 3, the interval starts at negative infinity and ends at 3, inclusive.

(−∞,3]

Final Answer

Domain:(−∞,3]

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