Determine if Odd, Even, or Neither f(x)=x^9

$f (x) = x^{9}$

Step 1

Find $f (- x)$ .

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

$f (- x) = {(- x)}^{9}$

Apply the product rule to $- x$ .

$f (- x) = {(- 1)}^{9} x^{9}$

Raise $- 1$ to the power of $9$ .

$f (- x) = - x^{9}$

Step 2

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

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

Since $- x^{9}$ $\neq$ $x^{9}$ , the function is not even.

The function is not even

Step 3

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

Multiply $- 1$ by $x^{9}$ .

$- f (x) = - x^{9}$

Since $- x^{9} = - x^{9}$ , the function is odd.

The function is odd

Step 4