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) 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),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

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.

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

If f(x-y), f(x).f(y) and f(x+ y) are in arithmatic progression and f(0) ne 0 then (for AA x and y ………

If f(x+y+z)=f(x) f(y) f(z) ne 0 for all x,y,z and f(2)=5, f'(0)=2, find f'(2).

If f(x+y+z)=f(x)f(y)f(z)ne0 , for all x, y, z and f(2)=4,f'(0)=3 , find f'(2) .