​Let f(x) = [x^2 - x] + |-x + [x] |, where x ∈ R and [t] denotes the greatest integer less than or equal to t. ​

Question

Let f(x) = [x² - x] + |-x + [x] |, where x ∈ \(\mathbb{R}\) and [t] denotes the greatest integer less than or equal to t. Then, f is 

(1) continuous at x = 0, but not continuous at x = 1 

(2) continuous at x = 0 and x = 1 

(3) not continuous at x = 0 and x = 1 

(4) continuous at x = 1, but not continuous at x = 0

Answer 1

(4) continuous at x = 1, but not continuous at x = 0

Here f(x) = [x(x-1)] + {x}

∴ f(x) is continuous at x = 1, discontinuous at x = 0