Determine if Odd, Even, or Neither f(x)=6x^5

$f (x) = 6 x^{5}$

Step 1

Find $f (- x)$ .

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

$f (- x) = 6 {(- x)}^{5}$

Apply the product rule to $- x$ .

$f (- x) = 6 ({(- 1)}^{5} x^{5})$

Raise $- 1$ to the power of $5$ .

$f (- x) = 6 (- x^{5})$

Multiply $- 1$ by $6$ .

$f (- x) = - 6 x^{5}$

Step 2

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

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

Since $- 6 x^{5}$ $\neq$ $6 x^{5}$ , the function is not even.

The function is not even

Step 3

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

Multiply $6$ by $- 1$ .

$- f (x) = - 6 x^{5}$

Since $- 6 x^{5} = - 6 x^{5}$ , the function is odd.

The function is odd

Step 4