Finite Math Examples

$f (x) = x \sin (x^{2})$

Step 1

Find $f (- x)$ .

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Step 1.1

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

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

Step 1.2

Apply the product rule to $- x$ .

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

Step 1.3

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

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

Step 1.4

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

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

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 $- x \sin (x^{2})$ $\neq$ $x \sin (x^{2})$ , 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

Remove parentheses.

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

Step 3.2

Since $- x \sin (x^{2}) = - x \sin (x^{2})$ , the function is odd.

The function is odd

Step 4