Find the Domain square root of 22x+33=x+7

Problem

√(,22*x+33)=x+7

Solution

1. Identify the restriction for the square root function, which requires the radicand (the expression inside the square root) to be non-negative.

22*x+33≥0

2. Solve the inequality for x by subtracting 33 from both sides.

22*x≥−33

3. Divide both sides by 22 to isolate x

x≥(−33)/22

4. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 11

x≥−3/2

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

[−3/2,∞)

Final Answer

Domain:[−3/2,∞)

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