If f(x) and g(x) are odd functions, then what type of function is y=f(x)g(x) ?

Question

Multiple Choice 

a) Odd

b) Even

c) Neither

d) Cannot be determined for sure

Answer 1

Add odd function is one where f(-x) = -f(x).

 

Since both f(x) and g(x) are odd, you know that f(-x)g(-x) = [-f(x)] [-g(x)] = f(x) g(x).  That means that f(x) g(x) is an even function.