Let f(x, y) be a periodic function satisfying `f(x, y) = f(2x + 2y, 2y-2x)` for all x, y; Define `g(x) = f(2^x,0)`. Show that g(x) is a periodic function with period 12.

Let f(x, y) be a periodic function satisfying the condition f(x, y) = f(2x + 2y), (2y - 2x) AA x, y in R . Now define a function g by g(x) = f(2^x, 0) . Then prove that g(x) is periodic function, find its period.

Let f(x, y) be a periodic function, satisfying the condition f(x, y) = f(2x+2y, 2y-2x) AA x , y in R and let g(x) be a function defined as g(x)=f(2^(x), 0) Prove that g(x) is a periodic function and find its period

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) =

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

Let f(x) is a polynomial satisfying f(x).f(y) = f(x) +f(y) + f(xy) - 2 for all x, y and f(2) = 1025, then the value of lim_(x->2) f'(x) is

Let f be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x) , for all x and y, where g(x) is a continuous function. Then f'(x) is :