Algebra Examples

$f (x) = 5 x$

Find $f (- x)$ .

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

$f (- x) = 5 (- x)$

Multiply $- 1$ by $5$ .

$f (- x) = - 5 x$

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

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

$- 5 x$ $\neq$ $5 x$

Since $- 5 x$ $\neq$ $5 x$ , the function is not even.

The function is not even

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

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Multiply $5$ by $- 1$ .

$- f (x) = - 5 x$

Since $- 5 x = - 5 x$ , the function is odd.

The function is odd