Question

The function f(x) = 2x^3 + 3x^2 is:

(a) even
(b) odd
(c) neither
(d) even and odd​

Answer 1

neither

Step-by-step explanation:

First we must determine if both x and -x are in the domain of the function

since it is a polynomial function our first condition is satisfied

Then we should calculate the image of -x :

2x(-x)^3 + 3*(-x)² = -2x^3+3x²

it is not equal to f(x) nor -f(x)

Answer 2

Answer:
d). Even and odd

Step-by-step explanation:
2x^3 = even
Since any number times 2 will be even
3x^2 = even/odd

Let’s assume x = 2
Then 3(2)^2 = 3 x 4 = 12 = even

Assume x = 3

3(3)^2 = 3 x 9 = 27 = odd

Now we know our equation has:

even + even/odd = even and odd

Ex: 2 + 2 = 4 = even
Ex: 2 + 3 = 5 = odd
So our equation can be equal to either even and odd