test the function f(x)=x(x+1)(x+2)^2 for oddness or evenness.?

Answer 1

f(-x) = -x (-x+1)(-x+2)^2
= x(x-1)(x-2)^2
the function is nither odd nor even

Answer 2

In this case you could do it just by testing values:

e.g. try f(1) and f(-1), you find they are neither the same nor opposites, and so the function is neither even nor odd.

OA more sophisticated method would be
f(-x) = -x(-x+1)(-x+2)

and then show that f(x) - f(-x) isn't zero, so it isn't even,
and f(x) + f(-x) isn't zero, so it isn't odd.

Yet again:

Even powers of x are even functions, odd powers are odd functions, and a mixture is neither. So, expand and see that it's a mixture.

Answer 3

I think that the value of f(x) must be even
if x is odd then x+1 is even so f(x) will be the value of multiplying 2 with a number
it is the same to if x is even

Answer 4

f(-x)=(-x)(-x+1)(-x+2)^2
=(x^2-x)(-x+2)^2
=(x^2)(-x+2)^2-x(-x+2)^2
since the squares are always positive the first term is positive
the second term is negative and so the function is odd

Answer 5

check
f(-x) = -x(-x+1) (-x+2)^2
now
f(x)=x(x+1)(x+2)^2
so it is not even and it is not odd
h