Find the Domain and Range ( square root of x-2)/(x-3)

$\frac{\sqrt{x - 2}}{x - 3}$

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

$x - 2 \geq 0$

Add $2$ to both sides of the inequality.

$x \geq 2$

Set the denominator in $\frac{\sqrt{x - 2}}{x - 3}$ equal to $0$ to find where the expression is undefined.

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

Interval Notation:

$[2, 3) \cup (3, \infty)$

Set-Builder Notation:

${x | x \geq 2, x \neq 3}$

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${y | y \neq 0}$

Determine the domain and range.

Domain: $[2, 3) \cup (3, \infty), {x | x \geq 2, x \neq 3}$

Range: $(- \infty, 0) \cup (0, \infty), {y | y \neq 0}$