Question:
Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.
Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.
Updated On: Feb 20, 2026
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Correct Answer: 2
Solution and Explanation
We need to check for discontinuity at doubtful points \( x \in I \).
At \( x = -1 \):
\( f(-1^+) = 1 + 0 = 1 \)
\( f(-1^-) = 2 + 1 = 3 \)
At \( x = 0 \):
\( f(0^+) = 0 + 0 = 0 \)
\( f(0^-) = 1 + 1 = 2 \)
At \( x = 1 \):
\( f(1^+) = 1 + 0 = 1 \)
\( f(1^-) = 0 + 1 = 1 \)
From the above calculations, discontinuity occurs at two points.
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