Question

If f(x) and g(x) be two given functions with all real numbers as their domain, then h(x) = [f(x) + f(−x)] [g(x) – g(−x)] is

(A)  An odd function

(B)  An odd function when both f and g are odd

(C)  An odd function when f is even and g is odd

(D)  None of these

Answer 1

Correct option  (A) An odd function

Explanation :

h(x) = [f(x) + f(−x)] [g(x) – g(−x)]

h(–x) = [f(–x) + f(x)] [g(–x) – g(x)] = –h(–x)

Therefore, h(x) is an odd function.