Find the Domain and Range f(x) = square root of 5x-10

$f (x) = \sqrt{5 x - 10}$

Step 1

Set the radicand in $\sqrt{5 x - 10}$ greater than or equal to $0$ to find where the expression is defined.

$5 x - 10 \geq 0$

Step 2

Solve for $x$ .

Add $10$ to both sides of the inequality.

$5 x \geq 10$

Divide each term in $5 x \geq 10$ by $5$ and simplify.

Divide each term in $5 x \geq 10$ by $5$ .

$\frac{5 x}{5} \geq \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{10}{5}$

Divide $x$ by $1$ .

$x \geq \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$x \geq 2$

Step 3

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

Interval Notation:

$[2, \infty)$

Set-Builder Notation:

${x | x \geq 2}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Step 5

Determine the domain and range.

Domain: $[2, \infty), {x | x \geq 2}$

Range: $[0, \infty), {y | y \geq 0}$

Step 6