Problem 17 - Precalculus 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 inequality

Since the expression under the square root cannot be negative, set up the inequality \(x-3 \geq 0\).

Step 2: Solve the inequality

To solve this inequality, add 3 to both sides to isolate x, resulting in \(x \geq 3\).

Step 3: Conclusion

So, the domain of function \(f(x) = \sqrt{x-3}\) is \(x \geq 3\). This means the function is defined for all real numbers greater than or equal to 3.