Let f (x) be an odd function for continuous at `x in R` If f(x) is continuous at x = a, prove that it is continous at x=-a

Let f(x) be an even function forall x in R If f(x) is continuous at x = a, prove that it is continuous at x = - a.

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 .

Show that f(x) = sinx is continuous on R .

Show that the function f(x) =x sub (1)/(x) , x ne 0 f(0) =0 is continuous at x = 0

Prove that the function f(x)= 5x-3 is continuous at x=0, at x= -3" and at " x=5 .

Examin the following functions for continuity. f(x)= x-5