Even function multiplied by odd function

The product of an even function and an odd function is an odd function. The quotient of two even functions is even, and the quotient of two odd functions is even.

1. Is the product of two odd functions even?
2. How do you find the sum of an even and odd function?
3. What function has both even and odd symmetry?

Is the product of two odd functions even?

The product of two odd functions is an even function. The product of an even function and an odd function is an odd function.

How do you find the sum of an even and odd function?

which is, again, a sum of an even and an odd function. If f(x) = e(x) + o(x) with e even and o odd, then changing x to –x gives f(-x) = e(-x) + o(-x) = e(x) – o(x). and o(x) = \fracf(x) - f(-x)2. Notice that since f is defined for -a \lt x \lt a, so is f(-x), and therefore so are e(x) and o(x).

What function has both even and odd symmetry?

The only function which is both even and odd is f(x) = 0, defined for all real numbers. This is just a line which sits on the x-axis. If you count equations which are not a function in terms of y, then x=0 would also be both even and odd, and is just a line on the y-axis.