Find the Domain g(x)=( square root of x-5)/(x-10)

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

Step 1

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

$x - 5 \geq 0$

Step 2

Add $5$ to both sides of the inequality.

$x \geq 5$

Step 3

Set the denominator in $\frac{\sqrt{x - 5}}{x - 10}$ equal to $0$ to find where the expression is undefined.

$x - 10 = 0$

Step 4

Add $10$ to both sides of the equation.

$x = 10$

Step 5

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

Interval Notation:

$[5, 10) \cup (10, \infty)$

Set-Builder Notation:

${x | x \geq 5, x \neq 10}$

Step 6