If `y=f(x)` satisfies `f(x+1)+f(z-1)=f(x+z) AA x, z in R` and `f(0)=0` and `f'(0)=4` then `f(2)` is equal to

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

Consider y = x^(2) and f (x) where f (x), is a differentiable function satisfying f (x+1) + f (z-1) =f (x+z) AA x , z in R and f (0) =0,f '(0) =4. If area bounded by curve y = x^(2) and y=f(x) is Delta, find the value of ((3)/(16) Delta).

Let f:R rarr R be a differentiable function satisfying 2f((x+y)/(2))-f(y)=f(x) AA x , y in R ,if f(0)=5 and f'(0)=-1 , then f(1)+f(2)+f(3) equals

If quad f'(0)=1AA x and y and f(x+y)=f(x)*f(y) then f(1) is equal to

If f satisfies the relation f(x+y)+f(x-y)=2f(x)f(y)AA x,y in K and f(0)!=0; then f(10)-f(-10)-

Let f(x)=x+f(x-1) for AA x in R.If f(0)=1, find f(100)