proving the function is even
Let f(x) be a function. prove that :
(a) g(x) =1/2[f(x)+f(-x)] is an even function
(b) h(x) = 1/2[f(x)-f(-x)] is an odd function
(c) hence show that every function can be written as a sum of an even function and odd function...
my approaches towards the question :
i know that even function will yield f(-x) = f(x)
and odd function will yield f(-x) = -f(x)
(a) g(-x) = 1/2[f(-x) + f(x)] = 0
(b) h(-x) = 1/2[f(-x)-f(x)] = 1/2[-2f(x)] = -f(x)
(c) i dunno...
plz help me .... thanx(Nerd)