Precalculus Examples

$f (x) = \frac{1}{4 x}$

Step 1

Find $f (- x)$ .

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Step 1.1

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

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

Step 1.2

Cancel the common factor of $1$ and $- 1$ .

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Step 1.2.1

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

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

Step 1.2.2

Move the negative in front of the fraction.

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

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

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 $- \frac{1}{4 x}$ $\neq$ $\frac{1}{4 x}$ , 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 $\frac{1}{4 x}$ .

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

Step 3.2

Since $- \frac{1}{4 x} = - \frac{1}{4 x}$ , the function is odd.

The function is odd

Step 4