Question

what is the domain of the function $y = \sqrt{x}$?
options:
$-\infty < x < \infty$
$0 \leq x < \infty$
$1 \leq x < \infty$
$0 < x < \infty$

Explanation:

Step1: Recall domain of square root

The square root function \( y = \sqrt{x} \) is defined when the radicand \( x \) is non - negative (since we are dealing with real - valued functions). So we need to find all real numbers \( x \) such that \( x\geq0 \).

Step2: Analyze the inequality

The inequality \( x\geq0 \) in interval notation is \( 0\leq x<\infty \) (because \( x \) can be 0 or any positive real number, and there is no upper bound on positive real numbers in the context of the square root of a non - negative real number).

Answer:

\( 0\leq x<\infty \) (the option with the inequality \( 0\leq x<\infty \))