Determine if Odd, Even, or Neither 1/(x^2+2)

$\frac{1}{x^{2} + 2}$

Step 1

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

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

Step 2

Find $f (- x)$ .

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

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

Simplify the denominator.

Apply the product rule to $- x$ .

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

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

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

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

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

Step 3

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

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

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

The function is even

Step 4