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),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)

Let f : R to R be a function given by f(x+y)=f(x)f(y) for all x , y in R If f(x) ne 0 for all x in R and f'(0) exists, then f'(x) equals

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2)) then:

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is

Let f:R in R be a function given by f(x+y)=f(x) f(y)"for all"x,y in R "If "(x) ne 0,"for all "x in R and f'(0)=log 2,"then "f(x)=