Homework SourseLet f and g be two odd functions Prove that a f g is an odd
Let f and g be two odd functions. Prove that:
(a) f + g is an odd function and (b) g o f is an odd function.
(a) f + g is an odd function and (b) g o f is an odd function.
Solution
f and g are odd => f(-x) = -f(x) => g(-x) = -g(x) To prove any function to be odd , we must prove p(-x) = -p(x) a) f + g (- x) f(-x) + g(-x) = -f(x) -g(x) = -(f + g ( x) ) (Proved) b) g o f (-x) = g o (- f(x) ) = - (g o f (x) )
