parity f(x)=x^5 — step-by-step solution

Let's study the parity of

x^{5}

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)}^{5}

⇥Let's evaluate:

{(- x)}^{5}

⇥ⓘ 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)}^{5}

- x^{5}

⇥

- x^{5}

f(-

x

) = -f(

x

): the function is odd

▶Parity: $odd$