Let f : R → R be defined as f(x) =

Question

Let f : \(\mathbb{R}\) → \(\mathbb{R}\) be defined as 

where a,b,c ∈\(\mathbb{R}\) and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true ? 

(A) There exists a,b,c  such that f is continuous of R . 

(B) If f is discontinuous at exactly one point, then a + b+ c = 1.

(C) If f is discontinuous at exactly one point, then a + b+ c ≠ 1.

(D) f is discontinuous at at least two points, for any values of a, b and c.

Answer 1

(C) If f is discontinuous at exactly one point, then a + b+ c ≠ 1.

f(x) is discontinuous at x = 1 

For continuous at x = 0; a = 1 

For continuous at x = 2; b + c = 1 

a + b + c = 2