If `f(x-y), f(x) f(y) and f(x+y) ` are in A.P. for all `x, y in R` and f(0)=0. Then,

If f (x-y), f (x) ,f (y) and f (x + y) are in A.P for all x,y in E and f (0) = 0 show that f ' (x) is even.

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

Let f be a real function such that f(x-y), f(x)f(y) and f(x+y) are in A.P. for all x,y, inR. If f(0)ne0, then

If f(x-y),f(x)*f(y),f(x+y) are in A.P for all x,y in R " and " f(0) ne 0 , then (a) f'(x) is an even function (b)f'(1)+f'(-1)=0 (c)f'(2)-f'(-2)=0 (d)f'(2)-f'(-2)=0

f(x - y), f(x) f(y), f(x + y) are in A.P. AA x, y and f(0) != 0 then

Le f : R to R and g : R to R be functions satisfying f(x+y) = f(x) +f(y) +f(x)f(y) and f(x) = xg (x) for all x , y in R . If lim_(x to 0) g(x) = 1 , then which of the following statements is/are TRUE ?