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

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

Step 1

Set the radicand in $\sqrt{4 x}$ greater than or equal to $0$ to find where the expression is defined.

$4 x \geq 0$

Step 2

Divide each term in $4 x \geq 0$ by $4$ and simplify.

Divide each term in $4 x \geq 0$ by $4$ .

$\frac{4 x}{4} \geq \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{0}{4}$

Divide $x$ by $1$ .

$x \geq \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x \geq 0$

Step 3

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4