Question

The domain of $f(x) = x^{1/2}$ is:

• A. (-\infty, 0]
• B. 0
• C. All real numbers
• D. [0, \infty)

Answer 1

Answer: (D)

[0, \infty)

Answer 2

The function given is $f(x) = x^{1/2}$. This can be rewritten as $f(x) = \sqrt{x}$.

For the square root of a number to be a real number, the number inside the square root must be non-negative (greater than or equal to zero). Therefore, for $f(x) = \sqrt{x}$ to be defined in the set of real numbers, the argument $x$ must satisfy:

$x \ge 0$

In interval notation, $x \ge 0$ is represented as $[0, \infty)$. This interval includes 0 and all positive real numbers extending to infinity.