JEE Main 2013 Mathematics question
Consider the function : f(x) = [x] + |1 − x|, −1 ≤ x ≤ 3 where [x] is the greatest integer function. Statement 1: f is not continuous at x = 0, 1, 2 and 3 Statement 2:
Answer: (1)
Solution
On [−1, 0), [x] = −1 and |1 − x| = 1 − x, so f = −x ✓. On [0, 1), f = 0 + 1 − x = 1 − x ✓. On [1, 2), f = 1 + x − 1 = x, not 1 + x. On [2, 3), f = 2 + x − 1 = x + 1, and f(3) = 3 + 2
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