Algebra Examples

$y = 2 x^{- 6}$

Step 1

Write $y = 2 x^{- 6}$ as a function.

$f (x) = 2 x^{- 6}$

Step 2

Simplify.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (x) = 2 (\frac{1}{x^{6}})$

Step 2.2

Combine $2$ and $\frac{1}{x^{6}}$ .

$f (x) = \frac{2}{x^{6}}$

Step 3

Find $f (- x)$ .

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Step 3.1

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

$f (- x) = \frac{2}{{(- x)}^{6}}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Apply the product rule to $- x$ .

$f (- x) = \frac{2}{{(- 1)}^{6} x^{6}}$

Step 3.2.2

Raise $- 1$ to the power of $6$ .

$f (- x) = \frac{2}{1 x^{6}}$

Step 3.2.3

Multiply $x^{6}$ by $1$ .

$f (- x) = \frac{2}{x^{6}}$

Step 4

A function is even if $f (- x) = f (x)$ .

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Step 4.1

Check if $f (- x) = f (x)$ .

Step 4.2

Since $\frac{2}{x^{6}} = \frac{2}{x^{6}}$ , the function is even.

The function is even

Step 5