Question

The domain of the function \( f(x) = \sqrt{x} \) is

• A. \( \mathbb{R} - \{0\} \)
• B. \( \mathbb{R}^+ \)
• C. \( \mathbb{R}^+ \cup \{0\} \)
• D. \( \mathbb{R} \)

Hint:

When working with square roots, the domain is limited to non-negative real numbers.

Answer 1

The Correct Option is C

Step 1: Understanding the function.
The function \( f(x) = \sqrt{x} \) is defined only for non-negative values of \( x \), because the square root of a negative number is not real. Therefore, the domain of this function is \( x \geq 0 \), which includes all non-negative real numbers.

Step 2: Conclusion.
Thus, the domain of the function is \( \mathbb{R}^+ \cup \{0\} \), corresponding to option (C).