Question

Find the domain of the function. $$y=\sqrt{x+5}$$

Short answer

The domain of the function \(y = \sqrt{x + 5}\) is \(x \geq -5\).

Step-by-step solution

Identify the expression under the square root

In the function \(y = \sqrt{x + 5}\), the expression under the square root is \(x + 5\).

Formulate an inequality

To find the domain, set the expression under the square root to be greater than or equal to 0. This will form an inequality. So \(x + 5 \geq 0\).

Solve for x

To find the domain, solve the inequality \(x + 5 \geq 0\). By subtracting 5 from both sides, we find \(x \geq -5\).