Question

find the domain of the function. v (x)=√(6 + x) write your answer as an inequality. or, you may instead click on \empty set\ or \all reals\ as the answer.

Explanation:

Step1: Recall domain of square root

For a function \( v(x)=\sqrt{u(x)} \), the expression inside the square root (\( u(x) \)) must be non - negative (i.e., \( u(x)\geq0 \)) to have real - valued outputs.
In the function \( v(x)=\sqrt{6 + x} \), we set the expression inside the square root, \( 6 + x \), greater than or equal to zero. So we have the inequality \( 6+x\geq0 \).

Step2: Solve the inequality

To solve \( 6 + x\geq0 \) for \( x \), we subtract 6 from both sides of the inequality.
\( 6+x - 6\geq0 - 6 \)
Simplifying both sides, we get \( x\geq - 6 \).

Answer:

\( x\geq - 6 \) (In the input box, we would use the inequality tool to write \( x\geq - 6 \), for example, select the \( \square\geq\square \) button, put \( x \) in the first square and \( - 6 \) in the second square.)