Find the Domain y = square root of 9x-7

$y = \sqrt{9 x - 7}$

Step 1

Set the radicand in $\sqrt{9 x - 7}$ greater than or equal to $0$ to find where the expression is defined.

$9 x - 7 \geq 0$

Step 2

Solve for $x$ .

Add $7$ to both sides of the inequality.

$9 x \geq 7$

Divide each term in $9 x \geq 7$ by $9$ and simplify.

Divide each term in $9 x \geq 7$ by $9$ .

$\frac{9 x}{9} \geq \frac{7}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} \geq \frac{7}{9}$

Divide $x$ by $1$ .

$x \geq \frac{7}{9}$

Step 3

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

Interval Notation:

$[\frac{7}{9}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{7}{9}}$

Step 4