Question

If f(x) = {(x, when X ∈ Q), (- X, when X ∉ Q), then f(x) is continuous at ­ 

(A) All rational numbers 

(B) Zero only 

(C) Zero and 1 only 

(D) No where

Answer 1

Answer is (B) Zero only

Let us first examine continuity at x = 0.

= a or -a, which is not unique.

⇒ f(a - 0) does not exist

⇒ f(x) is not continuous at a ∈ R₀.

Hence f(x) is continuous only at x = 0.