Is there a function who are both even and odd

we know even function is defined f(-a) = f(a) and odd function defined f(-a) = -f(a)
is there a function who are both even and odd ??

If a function were both odd and even, we'd get:
f(-a) = f(a) and f(-a) = -f(a) -----> f(a) = -f(a)

But if you were to plot the points (a, b) and (a, -b),
this would fail the vertical line test, unless b = 0

So function f(x) = 0 is both odd and even, since
f(-a) = 0
f(a) = 0
-f(a) = -0 = 0

No other functions can be both odd and even.

Mαthmφm

it is impossible

it is either odd or even, but it is not both