Let f(x) be a real valued function such that `f(0)=1/2` and f(x+y)=f(x)f(a-y)+f(y)f(a-x),`forall x,y in R`, then for some real a,

Let f (x) be a real vaued continuous function such that f (0) =1/2 and f(x+y) = f(x) f (4-y) + f(y) f (4-x ) AA x, y in R, then for some real a: a. f(x) is a periodic function b. f(x) is a constant function c. f(x)=1/2 d. f(x)=(cosx)/2

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) is

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

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

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1_ =a. Then , f (x) =

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1) =a. Then , f (x) =

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=