parity f(x)=x^2 — step-by-step solution

Let's study the parity of

x^{2}

with respect to

x

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

) =

{(- x)}^{2}

⇥Let's calculate:

{(- x)}^{2}

⇥ⓘ With an even integer exponent, the minus sign in the base disappears; with an odd integer exponent, it moves in front of the power:

{(- x)}^{2}

x^{2}

⇥

x^{2}

f(-

x

) = f(

x

): the function is even

▶Parity: $even$