Precalculus Examples

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

Step 1

Find $f (- x)$ .

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Step 1.1

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

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

Step 1.2

Apply the product rule to $- x$ .

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

Step 1.3

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

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

Step 1.4

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

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

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

The function is even

Step 3