Problem

Find the domain of the function \(f(x) = \sqrt{2x+3}\)

Answer

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Answer

We then divide both sides by 2 to solve for \(x\), which gives us: \(x \geq -\frac{3}{2}\)

Steps

Step 1 ：The value under the square root (radicand), \(2x+3\), must be greater than or equal to zero. Therefore, we set up the inequality as follows: \(2x+3 \geq 0\).

Step 2 ：To solve for \(x\), we first subtract 3 from both sides of the inequality to get: \(2x \geq -3\)

Step 3 ：We then divide both sides by 2 to solve for \(x\), which gives us: \(x \geq -\frac{3}{2}\)

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