Determine if Odd, Even, or Neither 4x^2+1

$4 x^{2} + 1$

Step 1

Write $4 x^{2} + 1$ as a function.

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

Step 2

Find $f (- x)$ .

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

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

Simplify each term.

Apply the product rule to $- x$ .

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

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

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

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

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

Step 3

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

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

$4 x^{2} + 1 = 4 x^{2} + 1$

Since $4 x^{2} + 1 = 4 x^{2} + 1$ , the function is even.

The function is even

Step 4