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`

Show that the function f(x)=2x-|x| is continuous at x=0.

Show that the function f(x)=2x-|x| is continuous at x=0 .

Show that f(x)=cos x is continuous for all values of x.

The function f(x) =sin|x| is continuous for all x

Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=0,s howt h a tf(x) is continuous at all xdot

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

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot 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)| le |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.

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

Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continuous then f'(x) is