JEE Advanced 2026 Mathematics question
Consider the function defined by
f(x) = (|x| + |x - 1|) x + [x x],
where [x sin x] is the greatest integer less than or equal to x sin x . Let α be the total number of points in the interval at which f is NOT continuous, and let β be the total number of points in the interval at which f is NOT differentiable. Then the value of α + β is .
Answer: 5
Solution
On the interval, x sin x is even, ≥ 0 and < π/2 ≈ 1.57, so [x sin x] changes only where x sin x = 1, i.e. at x ≈ ±1.114: two discontinuities, α = 2. The first part is continuous everywhere; is
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