parity f(x)=-4x^5+3x^2 — step-by-step solution

⚠ 4x is read as the product 4*x: for a power, write 4^x‖3x is read as the product 3*x: for a power, write 3^x

Let's study the parity of

- 4 x^{5} + 3 x^{2}

with respect to

x

⇥Let's find the domain of

- 4 x^{5} + 3 x^{2}

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

) =

- 4 \cdot {(- x)}^{5} + 3 \cdot {(- x)}^{2}

⇥Let's calculate:

- 4 \cdot {(- x)}^{5} + 3 \cdot {(- x)}^{2}

⇥ℹ

{(- x)}^{5}

- x^{5}

‖

{(- x)}^{2}

x^{2}

⇥

- 4 \cdot (- x^{5}) + 3 x^{2}

⇥

4 x^{5} + 3 x^{2}

f(-

x

) - f(

x

) =

8 x^{5}

and f(-

x

) + f(

x

) =

6 x^{2}

are nonzero polynomials: the function is neither even nor odd

▶Parity: $neither even nor odd$