parity f(x)= 1/(x^2+3) — step-by-step solution

Let's study the parity of

\frac{1}{x^{2} + 3}

with respect to

x

⇥Let's evaluate the domain of

\frac{1}{x^{2} + 3}

⇥ For the expression

\frac{1}{x^{2} + 3}

to be defined, we must have:

x^{2} + 3 \neq 0

⇥Solution obtained:

x \in ℝ

The domain is

x \in ℝ

This domain is symmetric about 0: if

x

is in the domain, -

x

is too

Replace

x

by -

x

: f(-

x

) =

\frac{1}{{(- x)}^{2} + 3}

⇥

\frac{1}{{(- x)}^{2} + 3}

⇥

\frac{1}{x^{2} + 3}

f(-

x

) = f(

x

): the function is even

▶Parity: $even$