Finite Math Examples

$f (x) = \ln (x^{2} + x)$

Step 1

Find $f (- x)$ .

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Step 1.1

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

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

Step 1.2

Remove parentheses.

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

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the product rule to $- x$ .

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

Step 1.3.2

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

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

Step 1.3.3

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

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

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 $\ln (x^{2} - x)$ $\neq$ $\ln (x^{2} + x)$ , the function is not even.

The function is not even

Step 3

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

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Step 3.1

Multiply $- 1$ by $\ln (x^{2} + x)$ .

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

Step 3.2

Since $\ln (x^{2} - x)$ $\neq$ $- \ln (x^{2} + x)$ , the function is not odd.

The function is not odd

Step 4

The function is neither odd nor even

Step 5