Question

f(x) = x - [x] is continuous at

(A) x = 0

(B) x = -1

(C) x = 1

(D) x = 1/2

Answer 1

Answer is (D) x = 1/2

We know that [x] is discontinuous at every integer.

Therefore it is continuous only at x = 1/2, while the function x is continuous at all points x = 0, -1, 1, 1/2.

Thus the given function is continuous only at x = 1/2.