Sum of Functions: Even, Odd, Neither?

[Mishie]

Why is the sum of even functions even, the sum of odd functions odd, and the sum of an even and an odd function neither even nor odd?? Thanks in advance!

 

[cristo]

This looks like homework. What do you think? What is an even/odd function? Can you try out, say, adding two even functions/ two odd functions together and see what happens? How about the case with one even and one odd? Can you generalise these?

 

[Mishie]

No, we have been working on even/odd functions at school, so I decided to do a bit of my own research and came across a site which had the generalizations that I've mentioned. I have tried to add two even/odd functions together and found that the answers match the generalization. I am just wondering why this is and how it works (if that makes sense).

 

[HallsofIvy]

Then before you ask questions about "even" and "odd" functions look up the definitions!
Google "even function" and you will finds loads of things.