Question

distinguish between odd and even functions .hence show the product of odd fuction and even function is a odd function

Answer 1

let f(x) be even (f(-x) = f(x)) and let g(x) be odd (g(-x) = -g(x))
let h(x) = f(x)g(x)
Lets show that h(x) is odd ( that is, lets show h(-x) = -h(x))
h(-x) = f(-x)g(-x) = f(x)(-g(x)) = -f(x)g(x) = -h(x)
Therefore h(-x) = -h(x), and the product of an even and odd function is odd.
done and done :)