Question

How do i determine if this function (x-4)(x+3)(2x-1) is even or odd?

Answer 1

if x = +1
(-3)(4)(1) = -12
if x = -1
(-5)(2)(-3) = +30
so f(-x) is NOT f(x) so not even
now is f(-x) = -f(x)
nope, 30 is not -(-12) so not odd

Answer 2

Can you do this in a way where you can just leave x as f(-x) instead of substituting it as 1?

Answer 3

Yes, but why bother ?

Answer 4

let x = a and then -a
and multiply the mess out and see if
f(-a) = f(a)
or if
f(-a) = - f(a)

Answer 5

I could have used x = 51375 or -51375
but no need
it has to work for ANY x to be odd or even

Answer 6

Okay, thanks for the clarification! It definitely is easier with your method, however my teacher wants it done in a certain way.