Algebra Examples

$g (x) = x^{4} + x$

Find $f (- x)$ .

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

$g (- x) = {(- x)}^{4} - x$

Remove parentheses.

$g (- x) = {(- x)}^{4} - x$

Simplify each term.

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Apply the product rule to $- x$ .

$g (- x) = {(- 1)}^{4} x^{4} - x$

Raise $- 1$ to the power of $4$ .

$g (- x) = 1 x^{4} - x$

Multiply $x^{4}$ by $1$ .

$g (- x) = x^{4} - x$

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

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

$x^{4} - x$ $\neq$ $x^{4} + x$

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

The function is not even

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

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Find $- f (x)$ .

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Multiply $x^{4} + x$ by $- 1$ .

$- f (x) = - (x^{4} + x)$

Apply the distributive property.

$- f (x) = - x^{4} - x$

Since $x^{4} - x$ $\neq$ $- x^{4} - x$ , the function is not odd.

The function is not odd

The function is neither odd nor even