Question

xvi) The

number
of
point f (x)
is[a rational, 0 if x is a irrrational] is continuous at?


a)1 b) infinity c) 2 d) 3​

Answer 1

Answer:

Let f be the function defined by f (x) = 1 if x is rational and f (x) = 0 if x is irrational. Then f is discontinuous at every point x. Take p ∈ Q and let (xn) be a sequence of irrationals converging to p. Then f (p) = 1 but f (xn))→ 0 and so f is discontinuous at p.