Problem 17 - College Algebra Essentials

Question

Find the domain of each function. $$f(x)=\sqrt{x-3}$$

Step-by-Step Solution

Answer

The domain of the function \(f(x) = \sqrt{x - 3}\) is \(x \geq 3\).

Step 1: Identify the Constraint from the Function

Start off by noting that the function contains a square root. A square root function domain is only defined for values \(\geq 0\), because we can't take the square root of a negative number in the real number system.

Step 2: Set up Inequality

To find the domain of the function, set the value under the square root, \(x-3\), to be greater than or equal to 0. This results in the inequality \(x - 3 \geq 0\) which we need to solve.

Step 3: Solve the Inequality

Solving the inequality \(x - 3 \geq 0\) gives \(x \geq 3\). This represents the set of all \(x\) values for which the function is defined.