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Finite Math Examples

f (x) = x^{4} - 6

$f (x) = x^{4} - 6$

Step 1

Find

f (- x)

$f (- x)$ .

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Step 1.1

Find

f (- x)

$f (- x)$ by substituting

- x

$- x$ for all occurrence of

x

$x$ in

f (x)

$f (x)$ .

f (- x) = {(- x)}^{4} - 6

$f (- x) = {(- x)}^{4} - 6$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the product rule to

- x

$- x$ .

f (- x) = {(- 1)}^{4} x^{4} - 6

$f (- x) = {(- 1)}^{4} x^{4} - 6$

Step 1.2.2

Raise

- 1

$- 1$ to the power of

4

$4$ .

f (- x) = 1 x^{4} - 6

$f (- x) = 1 x^{4} - 6$

Step 1.2.3

Multiply

x^{4}

$x^{4}$ by

1

$1$ .

f (- x) = x^{4} - 6

$f (- x) = x^{4} - 6$

f (- x) = x^{4} - 6

$f (- x) = x^{4} - 6$

f (- x) = x^{4} - 6

$f (- x) = x^{4} - 6$

Step 2

A function is even if

f (- x) = f (x)

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

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Step 2.1

Check if

f (- x) = f (x)

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

Step 2.2

Since

x^{4} - 6 = x^{4} - 6

$x^{4} - 6 = x^{4} - 6$ , the function is even.

The function is even

The function is even

Step 3

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$