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

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 .

Leg f(x+y)=f(x)+f(y) for all x,y in R, If f(x) is continuous at x=0, show that f(x) is continuous at all x.

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

if f(xy) = f(x) f(y) for all x and y and if f(x) is continuous at x = 1, then show that it is continuous for all x except 0

Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x) is continue at x=0,s howt h a tf(x) is continuous at all xdot