Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

The domain of the function$y=\sqrt{x}$is$\underset{¯}{\left\{x|x\le 0\right\}}$.

Short answer

The given sentence is False.

The true sentence isThe domain of the function$y=\sqrt{x}$is$\left\{x|x\ge 0\right\}$.

Step-by-step solution

Step 1. Determine whether the given sentence is true or false.

The domain of a function is the set of values of independent variable for which the function is defined.

Therefore, the domain of the function$y=\sqrt{x}$ is the set of values of x for which the function is defined.

Step 2. Explanation

As, for a square root to be a real number, the radicand cannot be negative. Therefore,$y=\sqrt{x}$ for to be defined, $x\ge 0$.

Therefore, the domain of the function$y=\sqrt{x}$ is $\left\{x|x\ge 0\right\}$.

Therefore, the given sentence is false.

Step 3. Write the true sentence.

Therefore, the true sentence is the domain of the function$y=\sqrt{x}$ is $\left\{x|x\ge 0\right\}$.