Find the Domain f(x) = square root of 3x+2

Problem

ƒ(x)=√(,3*x+2)

Solution

1. Identify the restriction for a square root function. For the function to be defined in the set of real numbers, the radicand (the expression inside the square root) must be greater than or equal to zero.

3*x+2≥0

2. Isolate the term containing x by subtracting 2 from both sides of the inequality.

3*x≥−2

3. Solve for x by dividing both sides by 3. Since 3 is a positive number, the inequality sign remains the same.

x≥−2/3

4. Express the domain in interval notation. The values of x start at −2/3 (inclusive) and extend to infinity.

[−2/3,∞)

Final Answer

Domain:[−2/3,∞)

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