To each open sphere S’(f(A)), there exists open sphere S(a,k) such that the function f[S(a, k)] is subset of S’(f(A)) iff

Correct option is C

To each open sphere S'( f(a)), there exists open sphere S(a, k) such that the function f[S(a, k)] is subset of S'(f(a)) iff the function f is continuous at 'a'.