Determine if Odd, Even, or Neither 2x^4+3

$2 x^{4} + 3$

Step 1

Write $2 x^{4} + 3$ as a function.

$f (x) = 2 x^{4} + 3$

Step 2

Find $f (- x)$ .

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

$f (- x) = 2 {(- x)}^{4} + 3$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = 2 ({(- 1)}^{4} x^{4}) + 3$

Raise $- 1$ to the power of $4$ .

$f (- x) = 2 (1 x^{4}) + 3$

Multiply $x^{4}$ by $1$ .

$f (- x) = 2 x^{4} + 3$

Step 3

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

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

Since $2 x^{4} + 3 = 2 x^{4} + 3$ , the function is even.

The function is even

Step 4