Thread: can a function be both even and odd?

can a function be both even and odd?

I believe f(x) = 0 is the only polynomial function that is both even and odd. I don't know about the other functions (exponential, logarithmic, logistic, trigonometric,...).


01

well that clears that up. and for logarithmic, exponential, trigo?

even ... f(-x) = f(x)

odd ... f(-x) = -f(x)

if even and odd, then f(x) = -f(x) ... what's that tell you?

do i take that as an absolute and true-in-all-cases 'no'? let's not be enigmatic please

Originally Posted by furor celtica

do i take that as an absolute and true-in-all-cases 'no'? let's not be enigmatic please

it's your exercise ... put some thought into it.

what function(s) is/are equal to its opposite?

even functions...

Originally Posted by furor celtica

even functions...

I believe he's looking for some kind of trig function (Hopefully what I'm thinking of isn't wrong either) ^^

Originally Posted by furor celtica

do i take that as an absolute and true-in-all-cases 'no'? let's not be enigmatic please

Forget (for the moment) that we are talking about functions and just consider the value y of f(x) at the point x.

As f is both odd and even y=f(x)=f(-x) and odd y=f(x)=-f(-x) and so:

y=-y.

Now what number/s (real or complex) is equal to minus times itself?

But this is true for every value taken by f.

CB