Find the Domain square root of 7+14x

Problem

√(,7+14*x)

Solution

1. Identify the restriction for a square root function. For the expression 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.

7+14*x≥0

2. Isolate the term containing x by subtracting 7 from both sides of the inequality.

14*x≥−7

3. Solve for x by dividing both sides by 14 Since 14 is a positive number, the inequality sign remains the same.

x≥(−7)/14

4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 7

x≥−1/2

5. Express the domain in interval notation. The values of x start at −1/2 (inclusive) and go to infinity.

[−1/2,∞)

Final Answer

Domain=[−1/2,∞)

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