Find the Domain f(x)=x/(x-7)

$f (x) = \frac{x}{x - 7}$

Set the denominator in $\frac{x}{x - 7}$ equal to $0$ to find where the expression is undefined.

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

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

Interval Notation:

$(- \infty, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \neq 7}$