Find the Domain of the Quotient of the Two Functions f(x)=5x-6 , g(x)=x-3

$f (x) = 5 x - 6$ , $g (x) = x - 3$

Step 1

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

$\frac{5 x - 6}{x - 3}$

Step 2

Set the denominator in $\frac{5 x - 6}{x - 3}$ equal to $0$ to find where the expression is undefined.

$x - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$x = 3$

Step 4

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

Interval Notation:

$(- \infty, 3) \cup (3, \infty)$

Set-Builder Notation:

${x | x \neq 3}$

Step 5