Finite Math Examples

$f (x) = - 5 x^{2} + | - 7 x |$

Step 1

Remove non-negative terms from the absolute value.

$f (x) = - 5 x^{2} + 7 | x |$

Step 2

Find $f (- x)$ .

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Step 2.1

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

$f (- x) = - 5 {(- x)}^{2} + 7 | - x |$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the product rule to $- x$ .

$f (- x) = - 5 ({(- 1)}^{2} x^{2}) + 7 | - x |$

Step 2.2.2

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

$f (- x) = - 5 (1 x^{2}) + 7 | - x |$

Step 2.2.3

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

$f (- x) = - 5 x^{2} + 7 | - x |$

Step 2.2.4

Make $- x$ positive.

$f (- x) = - 5 x^{2} + 7 | x |$

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 $- 5 x^{2} + 7 | x | = - 5 x^{2} + 7 | x |$ , the function is even.

The function is even

Step 4