If f and g are both odd functions defined on (-, ), what can be said about the evenness or oddness of (a) the sum f + g, (b) the product fg, and (c) the composition f g?
A) (a) odd, $~~~~~~~~$(b) even,$~~~~~~~~$ (c) odd
B) (a) even,$~~~~~~~~$ (b) even, $~~~~~~~~$(c) odd
C) (a) even, $~~~~~~~~$(b) odd, $~~~~~~~~$(c) odd
D) (a) odd, $~~~~~~~~$(b) even, $~~~~~~~~$(c) even
E) All three are odd.

Question

If f and g are both odd functions defined on (-,  ), what can be said about the evenness or oddness of (a) the sum f + g, (b) the product fg, and (c) the composition f  g?
A) (a) odd, $~~~~~~~~$(b) even,$~~~~~~~~$ (c) odd 
B) (a) even,$~~~~~~~~$ (b) even, $~~~~~~~~$(c) odd 
C) (a) even, $~~~~~~~~$(b) odd, $~~~~~~~~$(c) odd 
D) (a) odd, $~~~~~~~~$(b) even, $~~~~~~~~$(c) even 
E) All three are odd.

Quizplus · Accepted Answer

The Answer of If f and g are both odd functions defined on (-,  ), what can be said about the evenness or oddness of (a) the sum f + g, (b) the product fg, and (c) the composition f  g?
A) (a) odd, $~~~~~~~~$(b) even,$~~~~~~~~$ (c) odd 
B) (a) even,$~~~~~~~~$ (b) even, $~~~~~~~~$(c) odd 
C) (a) even, $~~~~~~~~$(b) odd, $~~~~~~~~$(c) odd 
D) (a) odd, $~~~~~~~~$(b) even, $~~~~~~~~$(c) even 
E) All three are odd.

If F and G Are Both Odd Functions Defined on (-