Question

Let E be an even function and O be an odd function. Determine the symmetry, if any, of the following function.

E (Dot) O

Answer 1

Remember that E(-x) = E(x) for all even functions (and all real numbers for x) and that O(-x) = - O(x) :

So for each let's plug in -x into the resulting equaiton and see what comes out: 

1) F(x) = E(x) * O(x) 

F(-x) = E(-x) * O(-x) = E(x) (- O(x)) = - E(x) * O(x) = -F(x), which means that F(x) is
an ODD function