Precalculus Examples

$f (x) = - \frac{1}{2} x^{4} + 5$

Step 1

Combine $x^{4}$ and $\frac{1}{2}$ .

$f (x) = - \frac{x^{4}}{2} + 5$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = - \frac{{(- x)}^{4}}{2} + 5$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the product rule to $- x$ .

$f (- x) = - \frac{{(- 1)}^{4} x^{4}}{2} + 5$

Step 2.2.2

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

$f (- x) = - \frac{1 x^{4}}{2} + 5$

Step 2.2.3

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

$f (- x) = - \frac{x^{4}}{2} + 5$

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 $- \frac{x^{4}}{2} + 5 = - \frac{x^{4}}{2} + 5$ , the function is even.

The function is even

Step 4