Determine if Odd, Even, or Neither 5x^2+x^4

$5 x^{2} + x^{4}$

Step 1

Write $5 x^{2} + x^{4}$ as a function.

$f (x) = 5 x^{2} + x^{4}$

Step 2

Find $f (- x)$ .

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

$f (- x) = 5 {(- x)}^{2} + {(- x)}^{4}$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = 5 ({(- 1)}^{2} x^{2}) + {(- x)}^{4}$

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

$f (- x) = 5 (1 x^{2}) + {(- x)}^{4}$

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

$f (- x) = 5 x^{2} + {(- x)}^{4}$

Apply the product rule to $- x$ .

$f (- x) = 5 x^{2} + {(- 1)}^{4} x^{4}$

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

$f (- x) = 5 x^{2} + 1 x^{4}$

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

$f (- x) = 5 x^{2} + x^{4}$

Step 3

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

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

Since $5 x^{2} + x^{4} = 5 x^{2} + x^{4}$ , the function is even.

The function is even

Step 4