Is there a function f such that f is both even and odd functions?

Answer 1

f=0

Answer 2

The absolute value function is even, since |-x| = |x|. The only function that is both even and odd is the constant function f(x)=C.

Edit: The other responses are correct. The only function that is both even and odd is the constant function f(x) = 0.

Answer 3

Even: f(-x) = f(x)
Odd: f(-x) = -f(x)

Sure: function from the space {0,1} => {0,1}

f(0) = 0
f(1) = 1

If you are speaking of a function over any larger set, then no:

If f is both even and odd f(x) = -f(x) for all values of x so 2f(x) = 0. If we have unique factorization then either 2 == 0 (the above example) or f(x) == 0.

Answer 4

it's easy to obtain such function
if f is even then f(x)=f(-x)
if f is odd then -f(x)=f(-x)
then we can concluse from above statements that such a funftion should meet the following property that f(x)=-f(x)then
2f(x)=0 and so f(x)=0 it means the zero function is the only one

Answer 5

Take f as

sin x for x<0,
cos x for x>=0

f is both even and odd over R. However, for any specified value, the function can be either even or odd.

For example x E (-pi, pi/2), f is odd in (-pi, 0) and even in [0, pi/2).

A constant function [ f(x)=c] is always even as f(-x)= f(x)=c. It has been wrongly pointed out to be an even f by one of the answerers, gp4rts.

Answer 6

Be specific

Impulse function is both odd & even

Every function can be divided into even and odd components

Sorry did not understand what you want.

Answer 7

Yes there is, it's the absolute value function right? Correct me if Iam wrong