If `f(x-y),f(x)f(y),a n df(x+y)` are in A.P. for all `x , y ,a n df(0)!=0,` then (a)`f(4)=f(-4)` (b)`f(2)+f(-2)=0` (c)`f^(prime)(4)+f^(prime)(-4)=0` (d)`f^(prime)(2)=f^(prime)(-2)`

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 in R and f(0)=0. Then,

If f(x+y)=f(x).f(y) for all real x,y and f(0)!=0, then the function g(x)=(f(x))/(1+{f(x)}^(2)) is:

Consider the function f:(-oo,\ oo)->(-oo,oo) defined by f(x)=(x^2-a x+1)/(x^2+a x+1),\ 0

f(x+(1)/(y))+f(x-(1)/(y))=2f(x)*f((1)/(y)) for all xy in R-{0} and f(0)=(1)/(2), then f(4) is

If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f(4)=2, then f'(4) is equal to

Let f(x+2y)=f(x)(f(y))^(2) for all x,y and f(0)=1. If f is derivable at x=0 then f'(x)=

Let y=f(x) be a parabola, having its axis parallel to the y-axis, which is touched by the line y=x at x=1. Then, (a) 2f(0)=1-f^(prime)(0) (b) f(0)+f^(prime)(0)+f^(0)=1 (c) f^(prime)(1)=1 (d) f^(prime)(0)=f^(prime)(1)