If f is a real valued function not identically zero, satisfying `f(x+ y)+ f (x-y) = 2f(x). f(y)` then f(x) is

f is a real-valued function not identically zero, satisfying f(x + y) + f(x - y) = 2f(x) ·f(y) AA x, y in R. f(x) is definitely a)odd b)even c)neither even nor odd d)none of these

Let f(x) be a real valued function not identically zero satisfies the equation,f(x+y^(n))=f(x)+(f(y))^(n) for all real x&y and f'(0) 1) is an odd natural number.Find f(10).

f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) for all yinR , Then

Let 'f' be a non-zero real valued continuous function satisfying f(x + y) = f(x), f(y) . f(y) for all x, y in R if f(2) = 9 , then f(6) =

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

For all rest numbers x and y, it is known as the real valued function f satisfies f (x) + f (y) = f (x + y). If f(1) = 7, then Sigma_(r=1 )^(100) f(r ) is equal to

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

A real valued function f(x) satisfies the functional equation f(x-y) = f(x) f(y) - f(a-x) f(a+y) , where a is a given constant and f(0)=1 , f(2a-x) =?