Question

Determine algebraically whether the function is even, odd, or neither even nor odd. (2 points)

Answer 1

Answer:

The function f(x) is neither even nor odd.

Step-by-step explanation:

The given function is

$f(x) = -3x^4 - 2x - 5$

A function is called an even function if

$f(-x) = f(x)$

A function is called an odd function if

$f(-x) = -f(x)$

Substitute x=-x in the given function, to check whether the function is even, odd, or neither even nor odd.

$f(-x) = -3(-x)^4 - 2(-x) - 5$

$f(-x) = -3(x)^4 + 2(x) - 5$

$f(-x) \neq f(x)$

$f(-x) \neq -f(x)$

Therefore the function f(x) is neither even nor odd.

Answer 2

Answer:

f(x) is neither odd nor even function

Step-by-step explanation:

we are given

$f(x)=-3x^4-2x-5$

Firstly, we will find f(-x)

we can replace x as -x

we get

$f(-x)=-3(-x)^4-2(-x)-5$

now, we can simplify it

$f(-x)=-3x^4+2x-5$

we can see that

it is neither equal to f(x) nor -f(x)

we know that

For even:

$f(-x)=f(x)$

For odd:

$f(-x)=-f(x)$

so, f(x) is neither odd nor even function