Finite Math Examples

$y = \frac{1}{- 8 x + 1}$

Step 1

Set the denominator in $\frac{1}{- 8 x + 1}$ equal to $0$ to find where the expression is undefined.

$- 8 x + 1 = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Subtract $1$ from both sides of the equation.

$- 8 x = - 1$

Step 2.2

Divide each term in $- 8 x = - 1$ by $- 8$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- 8 x = - 1$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 1}{- 8}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 1}{- 8}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 8}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{8}$

Step 3

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

Interval Notation:

$(- \infty, \frac{1}{8}) \cup (\frac{1}{8}, \infty)$

Set-Builder Notation:

${x | x \neq \frac{1}{8}}$

Step 4