Precalculus Examples

$f (x) = \frac{1}{x^{2}}$

Step 1

Find $f (- x)$ .

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Step 1.1

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

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

Step 1.2

Simplify the denominator.

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Step 1.2.1

Apply the product rule to $- x$ .

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

Step 1.2.2

Raise $- 1$ to the power of $2$ .

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

Step 1.2.3

Multiply $x^{2}$ by $1$ .

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

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 $\frac{1}{x^{2}} = \frac{1}{x^{2}}$ , the function is even.

The function is even

Step 3