Find the Domain g(x)=( square root of x-4)/(x-9)

$g (x) = \frac{\sqrt{x - 4}}{x - 9}$

Step 1

Set the radicand in $\sqrt{x - 4}$ greater than or equal to $0$ to find where the expression is defined.

$x - 4 \geq 0$

Step 2

Add $4$ to both sides of the inequality.

$x \geq 4$

Step 3

Set the denominator in $\frac{\sqrt{x - 4}}{x - 9}$ equal to $0$ to find where the expression is undefined.

$x - 9 = 0$

Step 4

Add $9$ to both sides of the equation.

$x = 9$

Step 5

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

Interval Notation:

$[4, 9) \cup (9, \infty)$

Set-Builder Notation:

${x | x \geq 4, x \neq 9}$

Step 6