parity f(x)=6x^3 — step-by-step solution

Let's study the parity of

6 x^{3}

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

) =

6 \cdot {(- x)}^{3}

⇥Let's calculate:

6 \cdot {(- x)}^{3}

⇥ⓘ Powers are computed before multiplications, additions and subtractions. 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)}^{3}

- x^{3}

⇥

6 \cdot (- x^{3})

⇥ⓘ The minus sign is placed in front of the product:

6 \cdot (- x^{3})

- 6 x^{3}

⇥

- 6 x^{3}

f(-

x

) = -f(

x

): the function is odd

▶Parity: $odd$