Find the Domain square root of xd = cube root of x+d

Problem

ƒ(x)=√(,x+d)=√(3,x+d)

Solution

1. Identify the constraints for the square root function. For a square root √(,g(x)) to be defined in the set of real numbers, the radicand must be non-negative.

x+d≥0

2. Identify the constraints for the cube root function. The cube root √(3,g(x)) is defined for all real numbers, so there are no additional restrictions from this part of the expression.

x∈ℝ

3. Solve the inequality for the variable x to find the specific interval.

x≥−d

4. Express the domain in interval notation based on the inequality.

[−d,∞)

Final Answer

Domain={[x∈ℝ,x≥−d]}

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