Finite Math Examples

$f (x) = \frac{4 x - 5}{x - 7}$

Step 1

Find $f (- x)$ .

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Step 1.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = \frac{4 (- x) - 5}{(- x) - 7}$

Step 1.2

Multiply $- 1$ by $4$ .

$f (- x) = \frac{- 4 x - 5}{- x - 7}$

Step 1.3

Factor $- 1$ out of $- 4 x$ .

$f (- x) = \frac{- (4 x) - 5}{- x - 7}$

Step 1.4

Rewrite $- 5$ as $- 1 (5)$ .

$f (- x) = \frac{- (4 x) - 1 \cdot 5}{- x - 7}$

Step 1.5

Factor $- 1$ out of $- (4 x) - 1 (5)$ .

$f (- x) = \frac{- (4 x + 5)}{- x - 7}$

Step 1.6

Rewrite $- (4 x + 5)$ as $- 1 (4 x + 5)$ .

$f (- x) = \frac{- 1 (4 x + 5)}{- x - 7}$

Step 1.7

Factor $- 1$ out of $- x$ .

$f (- x) = \frac{- 1 (4 x + 5)}{- (x) - 7}$

Step 1.8

Rewrite $- 7$ as $- 1 (7)$ .

$f (- x) = \frac{- 1 (4 x + 5)}{- (x) - 1 \cdot 7}$

Step 1.9

Factor $- 1$ out of $- (x) - 1 (7)$ .

$f (- x) = \frac{- 1 (4 x + 5)}{- (x + 7)}$

Step 1.10

Rewrite $- (x + 7)$ as $- 1 (x + 7)$ .

$f (- x) = \frac{- 1 (4 x + 5)}{- 1 (x + 7)}$

Step 1.11

Cancel the common factor.

$f (- x) = \frac{- 1 (4 x + 5)}{- 1 (x + 7)}$

Step 1.12

Rewrite the expression.

$f (- x) = \frac{4 x + 5}{x + 7}$

Step 2

A function is even if $f (- x) = f (x)$ .

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Step 2.1

Check if $f (- x) = f (x)$ .

Step 2.2

Since $\frac{4 x + 5}{x + 7}$ $\neq$ $\frac{4 x - 5}{x - 7}$ , the function is not even.

The function is not even

Step 3

A function is odd if $f (- x) = - f (x)$ .

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Step 3.1

Multiply $- 1$ by $\frac{4 x - 5}{x - 7}$ .

$- f (x) = - \frac{4 x - 5}{x - 7}$

Step 3.2

Since $\frac{4 x + 5}{x + 7}$ $\neq$ $- \frac{4 x - 5}{x - 7}$ , the function is not odd.

The function is not odd

Step 4

The function is neither odd nor even

Step 5