Determine if Odd, Even, or Neither 3x^6-1

$3 x^{6} - 1$

Step 1

Write $3 x^{6} - 1$ as a function.

$f (x) = 3 x^{6} - 1$

Step 2

Find $f (- x)$ .

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

$f (- x) = 3 {(- x)}^{6} - 1$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = 3 ({(- 1)}^{6} x^{6}) - 1$

Raise $- 1$ to the power of $6$ .

$f (- x) = 3 (1 x^{6}) - 1$

Multiply $x^{6}$ by $1$ .

$f (- x) = 3 x^{6} - 1$

Step 3

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

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

Since $3 x^{6} - 1 = 3 x^{6} - 1$ , the function is even.

The function is even

Step 4