Let `f(x+y)=f(x)+f(y)` for all `xa n dydot` If the function `f(x)` is continuous at `x=0,` show that `f(x)` is continuous for all `xdot`

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.

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.

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

if f(x+y)=f(x)+f(y)+c, for all real x and y and f(x) is continuous at x=0 and f'(0)=-1 then f(x) equals to

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 :

A function f(x) satisfies the following property: f(x.y)=f(x)f(y). Show that the function f(x) is continuous for all values of x if it is continuous at x=1

Statement-1: If |f(x)|<=|x| for all x in R then |f(x)| is continuous at 0. Statement-2: If f(x) is continuous then |f(x)| is also continuous.