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Odd and even functions

Yankel

Active member
Jan 27, 2012
398
Hello

I have a theoretical question. When I check if a function is odd or even, I usually check:

f(x)=f(-x) or f(-x)=-f(x)

someone told me today that before checking it, I first need to check the symmetry over the Y axis, and if the function is not symmetric over Y, there is no point of checking for odd or even.

Can someone explain this to me, and give a simple example of how to check for symmetry ?

thanks !
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
If f(-x) = f(x), then it is symmetric about the y-axis, i.e., it is even. I think your method is best.
 

Mr Fantastic

Member
Jan 26, 2012
66
Hello

I have a theoretical question. When I check if a function is odd or even, I usually check:

f(x)=f(-x) or f(-x)=-f(x)

someone told me today that before checking it, I first need to check the symmetry over the Y axis, and if the function is not symmetric over Y, there is no point of checking for odd or even.

Can someone explain this to me, and give a simple example of how to check for symmetry ?

thanks !
Think about the transformations to f(x) represented by f(-x) and -f(x) .....