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Count the points of discontinuity of a function with [x] or |x|

This type of question, asked 5 times: 9 May 2023 S2, 15 May 2023 S1, 9 May 2024 S1, 18 Apr 2026 S1, 13 May 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    9 May 2023 S2

    147
    Let f(x)=[x[x2]]f(x) = \left[x\left[\frac{x}{2}\right]\right], for −10<x<10-10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to

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  2. Question 2

    15 May 2023 S1

    107
    Let f:[−1,3]→Rf:[-1,3]\to\mathbb{R} be defined as f(x)={∣x∣+[x],−1≤x<1x+∣x∣,1≤x<2x+[x],2≤x≤3f(x) = \begin{cases}|x|+[x],&-1\leq x<1\\x+|x|,&1\leq x<2\\x+[x],&2\leq x\leq3\end{cases} where [t][t] denotes the greatest integer function. Then ff is discontinuous at

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  3. Question 3

    9 May 2024 S1

    142
    The number of discontinuities of the greatest integer function f(x)=[x]f(x)=[x], x∈(−72,100)x\in\left(-\frac{7}{2},100\right)

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  4. Question 4

    18 Apr 2026 S1

    73
    The number of point / points where the function f(x)=1x2−5∣x∣+6f(x) = \dfrac{1}{x^2 - 5|x| + 6} is discontinuous is......

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  5. Question 5

    13 May 2026 S1

    70
    The number of points of discontinuity of the function f(x)=1log⁡∣x2−1∣f(x) = \dfrac{1}{\log|x^2 - 1|} (where ∣⋅∣|\cdot| denotes the modulus function) is:

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