Find the Domain and Range f(x) = square root of 2x-6

$f (x) = \sqrt{2 x - 6}$

Set the radicand in $\sqrt{2 x - 6}$ greater than or equal to $0$ to find where the expression is defined.

$2 x - 6 \geq 0$

Solve for $x$ .

Add $6$ to both sides of the inequality.

$2 x \geq 6$

Divide each term in $2 x \geq 6$ by $2$ and simplify.

Divide each term in $2 x \geq 6$ by $2$ .

$\frac{2 x}{2} \geq \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{6}{2}$

Divide $x$ by $1$ .

$x \geq \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x \geq 3$

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

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${x | x \geq 3}$

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Determine the domain and range.

Domain: $[3, \infty), {x | x \geq 3}$

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