Question

show that there exists a unique function whose domain is {x∈R} and which is both even and odd.

Answer 1

my guess is \(f(x)=0\) is both
showing it is unique is the hard part

Answer 2

but not really that hard

Answer 3

suppose there is an \(x\) for which \(f(x)=a\neq 0\)
then \(f(-x)=a\) since \(f\) is even and also \(f(-x)=-a\) since \(f\) is odd, and therefore \(a=-a\) which shows \(a=0\) contradicting the assumption

Answer 4

that's kinda funny though :P

Answer 5

in a funny sort of way, yes