Precalculus Examples

$f (x) = \sin^{2} (x)$

Step 1

Find $f (- x)$ .

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Step 1.1

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

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

Step 1.2

Since $\sin (- x)$ is an odd function, rewrite $\sin (- x)$ as $- \sin (x)$ .

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

Step 1.3

Apply the product rule to $- \sin (x)$ .

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

Step 1.4

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

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

Step 1.5

Multiply $\sin^{2} (x)$ by $1$ .

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

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 $\sin^{2} (x) = \sin^{2} (x)$ , the function is even.

The function is even

Step 3