Precalculus Examples

$y = \frac{1}{\sec^{3} (x)}$

Step 1

Write $y = \frac{1}{\sec^{3} (x)}$ as a function.

$f (x) = \frac{1}{\sec^{3} (x)}$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = \frac{1}{\sec^{3} (- x)}$

Step 2.2

Since $\sec (- x)$ is an even function, rewrite $\sec (- x)$ as $\sec (x)$ .

$f (- x) = \frac{1}{\sec^{3} (x)}$

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 $\frac{1}{\sec^{3} (x)} = \frac{1}{\sec^{3} (x)}$ , the function is even.

The function is even

Step 4