If `f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2,` then find `f(x)dot`

If f((x+2y)/3)=(f(x)+2f(y))/3\ AA\ x ,\ y in R and f^(prime)(0)=1 , f(0)=2 , then find f(x) .

If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in R , and f(0)=3a n df^(prime)(0)=2, then the period of "sin"(f(x)) is (a)2pi (b) pi (c) 3pi (d) 4pi

Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot

Let f((x+y)/(2))=(f(x)+f(y))/(2),x,y in R, if f'(0)=-1, then f'((x)/(2))=

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

f((x+y)/(2))=(f(x)+f(y))/(2)AA x,y in R and f(0)=1 and f'(0)=-1 and function is differentiable for all x, then find f(x) .

If f((x + 2y)/3)=(f(x) + 2f(y))/3 AA x, y in R and f(x) is continuous at x = 0. Prove that f(x) is continuous for all x in R.

If f((x)/(y))=(f(x))/(f(y)),AA y,f(y)!=0 and f'(1)=2, find f(x)