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 (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 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 .

Examine whether the function f given by f(x)= x^2 is continuous at x= 0.

f(x) is an even function on R and f(x) is increasing on [2,6]. Then

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

Is the function defined by f(x)= x^(2)-sin x+5 continuous at x= pi ?

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.