Find the Domain y=4 square root of 2x+7

$y = 4 \sqrt{2 x + 7}$

Step 1

Set the radicand in $\sqrt{2 x + 7}$ greater than or equal to $0$ to find where the expression is defined.

$2 x + 7 \geq 0$

Step 2

Solve for $x$ .

Subtract $7$ from both sides of the inequality.

$2 x \geq - 7$

Divide each term in $2 x \geq - 7$ by $2$ and simplify.

Divide each term in $2 x \geq - 7$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 7}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{7}{2}$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[- \frac{7}{2}, \infty)$

Set-Builder Notation:

${x | x \geq - \frac{7}{2}}$

Step 4