Question

Consider the function f(x) = [(x{x} + 1, 0 ≤ x < 1), (2 - {x}, 1 ≤ x ≤ 2) where {x} denotes the fractional part function. Which one of the following statements is NOT correct?

(A) lim_(x →1) f(x) exists

(B) f(0) ≠ f(2)

(C) f (x) is continuous in [0, 2] 

(D) f(x) is differentiable in [0, 1) 

Answer 1

Answer is (C) f (x) is continuous in [0, 2]

f(1⁺)= f(1^-) = f(1) = 2

f(0)= 1, f(2) = 2 

f(2-) = 1; f(2) = 2 

⇒ f is not continuous at x = 2