can a function be both even and odd?
Last edited by CaptainBlack; Aug 7th 2009 at 12:35 AM.
Reason: Because I can
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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,...).
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?
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:
Now what number/s (real or complex) is equal to minus times itself?
But this is true for every value taken by f.
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