Finite Math Examples

$f (x) = - 1$ , $g (x) = 2 x + 1$

Step 1

Find the quotient of the functions.

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Step 1.1

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

$\frac{- 1}{2 x + 1}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{1}{2 x + 1}$

Step 2

Set the denominator in $\frac{1}{2 x + 1}$ equal to $0$ to find where the expression is undefined.

$2 x + 1 = 0$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Step 3.2

Divide each term in $2 x = - 1$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 4

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

Interval Notation:

$(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, \infty)$

Set-Builder Notation:

${x | x \neq - \frac{1}{2}}$

Step 5