Problem 18 - Precalculus Essentials

Question

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

Step-by-Step Solution

Answer

The domain of the function \(f(x) = \sqrt{x+2}\) is \(x \geq -2\), meaning the function is defined for any real number x greater than or equal to -2.

Step 1: Write down the function

The function given is \(f(x) = \sqrt{x+2}\).

Step 2: Set the argument under the square root greater than or equal to zero

For a function to be in the real number domain, the equation inside the square root must be greater than or equal to 0. Therefore, set the equation \(x+2 \geq 0\).

Step 3: Solve for \(x\)

Subtract 2 from both sides of this inequality to isolate x. That gives us \(x \geq -2\).