Precalculus Examples

Let $f (x) = 3 x - 6$ and $g (x) = x - 2$ Find $\frac{f}{g}$ and its domain.

Step 1

Replace the function designators in $f$ with the actual functions.

$3 x - 6$

Step 2

Replace the function designators in $g$ with the actual functions.

$x - 2$

Step 3

Rewrite $\frac{f}{g}$ .

$\frac{3 x - 6}{x - 2}$

Step 4

Set the denominator in $\frac{3 x - 6}{x - 2}$ equal to $0$ to find where the expression is undefined.

$x - 2 = 0$

Step 5

Add $2$ to both sides of the equation.

$x = 2$

Step 6

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

Interval Notation:

$(- \infty, 2) \cup (2, \infty)$

Set-Builder Notation:

${x | x \neq 2}$

Step 7