Find the Domain y = square root of 1+6x

$y = \sqrt{1 + 6 x}$

Step 1

Set the radicand in $\sqrt{1 + 6 x}$ greater than or equal to $0$ to find where the expression is defined.

$1 + 6 x \geq 0$

Step 2

Solve for $x$ .

Subtract $1$ from both sides of the inequality.

$6 x \geq - 1$

Divide each term in $6 x \geq - 1$ by $6$ and simplify.

Divide each term in $6 x \geq - 1$ by $6$ .

$\frac{6 x}{6} \geq \frac{- 1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{- 1}{6}$

Divide $x$ by $1$ .

$x \geq \frac{- 1}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{1}{6}$

Step 3

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

Interval Notation:

$[- \frac{1}{6}, \infty)$

Set-Builder Notation:

${x | x \geq - \frac{1}{6}}$

Step 4