Finite Math Examples

f (x) = 2 \cdot \frac{x}{1 - x}

$f (x) = 2 \cdot \frac{x}{1 - x}$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Set the denominator in

\frac{x}{1 - x}

$\frac{x}{1 - x}$ equal to

0

$0$ to find where the expression is undefined.

1 - x = 0

$1 - x = 0$

Step 1.2

Solve for

x

$x$ .

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Step 1.2.1

Subtract

1

$1$ from both sides of the equation.

- x = - 1

$- x = - 1$

Step 1.2.2

Divide each term in

- x = - 1

$- x = - 1$ by

- 1

$- 1$ and simplify.

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Step 1.2.2.1

Divide each term in

- x = - 1

$- x = - 1$ by

- 1

$- 1$ .

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

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

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Dividing two negative values results in a positive value.

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

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

Step 1.2.2.2.2

Divide

x

$x$ by

1

$1$ .

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

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

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

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

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide

- 1

$- 1$ by

- 1

$- 1$ .

x = 1

$x = 1$

x = 1

$x = 1$

x = 1

$x = 1$

x = 1

$x = 1$

Step 1.3

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

(- \infty, 1) \cup (1, \infty)

$(- \infty, 1) \cup (1, \infty)$

Set-Builder Notation:

{x | x \neq 1}

${x | x \neq 1}$

Interval Notation:

(- \infty, 1) \cup (1, \infty)

$(- \infty, 1) \cup (1, \infty)$

Set-Builder Notation:

{x | x \neq 1}

${x | x \neq 1}$

Step 2

Since the domain is not all real numbers,

2 \cdot \frac{x}{1 - x}

$2 \cdot \frac{x}{1 - x}$ is not continuous over all real numbers.

Not continuous

Step 3