Show that `f(x)=|x|` is continuous at x=0

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

show that f(x) =|x| is continuous but not differentiable at x =0

Show that f(x)=x-|x|,x inR is continuous at x = 0.

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.

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