Find the Domain y=2 square root of 2x+8

$y = 2 \sqrt{2 x + 8}$

Step 1

Set the radicand in $\sqrt{2 x + 8}$ greater than or equal to $0$ to find where the expression is defined.

$2 x + 8 \geq 0$

Step 2

Solve for $x$ .

Subtract $8$ from both sides of the inequality.

$2 x \geq - 8$

Divide each term in $2 x \geq - 8$ by $2$ and simplify.

Divide each term in $2 x \geq - 8$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 8}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x \geq - 4$

Step 3

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

Interval Notation:

$[- 4, \infty)$

Set-Builder Notation:

${x | x \geq - 4}$

Step 4