Find the Domain of the Quotient of the Two Functions f(x)=3x-6 g(x)=x-2

$f (x) = 3 x - 6$ $g (x) = x - 2$

Step 1

Find the quotient of the functions.

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

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

Simplify.

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{x - 2}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{x - 2}$

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{3 (x - 2)}{x - 2}$

Divide $3$ by $1$ .

$3$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

Find the Domain of the Quotient of the Two Functions f(x)=3x-6 g(x)=x-2

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