Let `f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0` If `f (x)` is continous at `x =0,` then ` f (x)` is continuous at :

Let f(x+y)=f(x)+f(y)AA x, y in R If f(x) is continous at x = 0, then f(x) is continuous at

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.

Let f(x+y) = f(x) + f(y) for all x and y. If the function f (x) is continuous at x = 0 , then show that f (x) is continuous at all x.

if f(x+y)=f(x)+ f(y) for all x and y and if f(x) is continuous at x=0, show that f(x) is continuous everywhere.

Let f(x+y)=f(x)+f(y) for all x and y If the function f(x) is continuous at x=0 show that f(x) is continuous for all x

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

Let f be a function defined on R such that f(x + y) = f (x) + f(y) AA x,y in R . If is continuous at x = 0 , Prove that it is continuous on R .

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