Precalculus Examples

$f (x) = \log_{3} (x^{8})$

Step 1

Find $f (- x)$ .

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Step 1.1

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

$f (- x) = \log_{3} ({(- x)}^{8})$

Step 1.2

Apply the product rule to $- x$ .

$f (- x) = \log_{3} ({(- 1)}^{8} x^{8})$

Step 1.3

Raise $- 1$ to the power of $8$ .

$f (- x) = \log_{3} (1 x^{8})$

Step 1.4

Multiply $x^{8}$ by $1$ .

$f (- x) = \log_{3} (x^{8})$

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 $\log_{3} (x^{8}) = \log_{3} (x^{8})$ , the function is even.

The function is even

Step 3