Find the Domain Y = square root of 5X-10

$Y = \sqrt{5 X - 10}$

Step 1

Factor $5$ out of $5 X - 10$ .

Factor $5$ out of $5 X$ .

$Y = \sqrt{5 (X) - 10}$

Factor $5$ out of $- 10$ .

$Y = \sqrt{5 X + 5 \cdot - 2}$

Factor $5$ out of $5 X + 5 \cdot - 2$ .

$Y = \sqrt{5 (X - 2)}$

Step 2

Set the radicand in $\sqrt{5 (X - 2)}$ greater than or equal to $0$ to find where the expression is defined.

$5 (X - 2) \geq 0$

Step 3

Solve for $X$ .

Divide each term in $5 (X - 2) \geq 0$ by $5$ and simplify.

Divide each term in $5 (X - 2) \geq 0$ by $5$ .

$\frac{5 (X - 2)}{5} \geq \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (X - 2)}{5} \geq \frac{0}{5}$

Divide $X - 2$ by $1$ .

$X - 2 \geq \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$X - 2 \geq 0$

Add $2$ to both sides of the inequality.

$X \geq 2$

Step 4

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

Interval Notation:

$[2, \infty)$

Set-Builder Notation:

${X | X \geq 2}$

Step 5