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Number of points where a function built from modulus terms is not continuous or not differentiable

This type of question, asked 6 times: 2021 Paper 3, 2021 Paper 22, 29 Jul 2022, 31 Jan 2024, 1 Feb 2024, 4 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 3

    86
    The number of points, at which the function f(x)=∣2x+1∣−3∣x+2∣+∣x2+x−2∣,x∈Rf(x) = |2x + 1| - 3|x + 2| +\left| x^{2}+ x - 2 \right|,x \in R is not differentiable, is

  2. Question 2

    2021 Paper 22

    67
    The function f(x)=∣x2−2x−3∣⋅e∣9x2−12x+4∣f(x)=\left|x^{2}-2x-3\right|\cdot e^{\left|9x^{2}-12x+4\right|} is not differentiable at exactly:

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  3. Question 3

    29 Jul 2022

    78
    The number of points, where the function f:R→R,f(x)=∣x−1∣cos⁡∣x−2∣sin⁡∣x−1∣+f:R \rightarrow R,f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x−3)∣x2−5x+4∣(x - 3)\left| x^{2}- 5x + 4 \right|, is NOT differentiable, is :

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  4. Question 4

    31 Jan 2024

    164
    Consider the function f:(0,∞)→Rf:(0,\infty) \rightarrow R defined by f(x)=e−∣log⁡ex∣f(x) =e^{-\left| \log_{e}x \right|}. If mm and nn be respectively the number of points at which ff is not continuous and ff is not differentiable, then m+nm + n is

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  5. Question 5

    1 Feb 2024

    151
    Let f(x)=∣2x2+5∣x∣−3∣,x∈Rf(x) =\left| 2x^{2}+ 5 \right|x| - 3|,x \in R. If mm and nn denote the number of points where ff is not continuous and not differentiable respectively, then m+nm + n is equal to:

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  6. Question 6

    4 Apr 2026 S2

    72
    Let f(x)={ex−1,x<0x2−5x+6,x≥0f(x) = \left\{ \begin{matrix} e^{x - 1} & ,x < 0 \\ x^{2} - 5x + 6 & ,x \geq 0 \end{matrix} \right. and g(x)=f(∣x∣)+∣f(x)∣g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are α\alpha and β\beta respectively, then α+β\alpha + \beta is equal to ____\_\_\_\_