Precalculus Examples

$f (x) = f (- x)$

Step 1

Rewrite using the commutative property of multiplication.

$f (x) = - f x$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = - f (- x)$

Step 2.2

Rewrite using the commutative property of multiplication.

$f (- x) = - 1 \cdot (- 1 f x)$

Step 2.3

Multiply $- 1$ by $- 1$ .

$f (- x) = 1 f x$

Step 2.4

Multiply $f$ by $1$ .

$f (- x) = f x$

Step 3

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

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Step 3.1

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

Step 3.2

Since $f x$ $\neq$ $- f x$ , the function is not even.

The function is not even

Step 4

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

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Step 4.1

Multiply $- (- f x)$ .

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Step 4.1.1

Multiply $- 1$ by $- 1$ .

$- f (x) = 1 (f x)$

Step 4.1.2

Multiply $f$ by $1$ .

$- f (x) = f x$

Step 4.2

Since $f x = f x$ , the function is odd.

The function is odd

Step 5