Question

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

Explanation:

Step1: Recall domain of square root function

The square root function \( y = \sqrt{x} \) is defined when the expression inside the square root (the radicand) is non - negative. So we need \( x\geq0 \).

Step2: Analyze the inequality

The inequality \( x\geq0 \) can be written in interval notation as \( 0\leq x<\infty \) (since \( x \) can be 0 or any positive real number up to infinity). The other options: \( 0 < x<\infty \) excludes 0 (but \( \sqrt{0}=0 \) is defined), \( -\infty < x<\infty \) includes negative numbers (and square root of negative numbers is not real), and \( 1\leq x<\infty \) excludes values between 0 and 1 (but \( \sqrt{0.25} = 0.5 \) is defined).

Answer:

\( 0\leq x<\infty \)