Find the Domain sixth root of 10+10z

Problem

√(6,10+10*z)

Solution

1. Identify the condition for the domain of an even root. For any function ƒ(z)=√(n,g(z)) where n is an even integer, the radicand must be greater than or equal to zero.

2. Set up the inequality based on the radicand of the sixth root.

10+10*z≥0

3. Subtract 10 from both sides of the inequality to isolate the term containing z

10*z≥−10

4. Divide both sides by 10 to solve for z Since 10 is a positive number, the inequality sign remains the same.

z≥−1

5. Express the domain in interval notation. The values of z start at −1 (inclusive) and go to infinity.

[−1,∞)

Final Answer

Domain:z≥−1

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