Problem 21 - College Algebra Essentials

Question

Find the domain of each function. $$g(x)=\sqrt{5 x+35}$$

Step-by-Step Solution

Answer

The domain of the function \(g(x)=\sqrt{5x+35}\) is \(x \geq -7\). This is because the value under the square root must be non-negative.

Step 1: Set up the inequality

The original function \(g(x)=\sqrt{5x+35}\) is only defined when the value underneath the square root is non-negative. This means we can set up the inequality: \(5x+35 \geq 0\)

Step 2: Simplify the inequality

Solving for x in this inequality is simple algebra. First, subtract 35 from both sides to get: \(5x \geq -35\)

Step 3: Solve the inequality

Next, divide both sides by 5 to isolate x: \(x \geq -7\)