Find the Domain y = square root of 13x-65

$y = \sqrt{13 x - 65}$

Step 1

Set the radicand in $\sqrt{13 x - 65}$ greater than or equal to $0$ to find where the expression is defined.

$13 x - 65 \geq 0$

Step 2

Solve for $x$ .

Add $65$ to both sides of the inequality.

$13 x \geq 65$

Divide each term in $13 x \geq 65$ by $13$ and simplify.

Divide each term in $13 x \geq 65$ by $13$ .

$\frac{13 x}{13} \geq \frac{65}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} \geq \frac{65}{13}$

Divide $x$ by $1$ .

$x \geq \frac{65}{13}$

Simplify the right side.

Divide $65$ by $13$ .

$x \geq 5$

Step 3

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

Interval Notation:

$[5, \infty)$

Set-Builder Notation:

${x | x \geq 5}$

Step 4