Finite Math Examples

$f (x) = 2 x + 2$ , $h (x) = 2 x$

Step 1

Find the quotient of the functions.

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Step 1.1

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

$\frac{2 x + 2}{2 x}$

Step 1.2

Cancel the common factor of $2 x + 2$ and $2$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 2}{2 x}$

Step 1.2.2

Factor $2$ out of $2$ .

$\frac{2 (x) + 2 \cdot 1}{2 x}$

Step 1.2.3

Factor $2$ out of $2 (x) + 2 (1)$ .

$\frac{2 (x + 1)}{2 x}$

Step 1.2.4

Cancel the common factors.

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Step 1.2.4.1

Factor $2$ out of $2 x$ .

$\frac{2 (x + 1)}{2 (x)}$

Step 1.2.4.2

Cancel the common factor.

$\frac{2 (x + 1)}{2 x}$

Step 1.2.4.3

Rewrite the expression.

$\frac{x + 1}{x}$

Step 2

Set the denominator in $\frac{x + 1}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 3

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 4