The number of points of discontinuity of $f (x)$ where $f (x) = ∣ ∣ ∣ ∣ ∣ | x + [x] | - 3 [x] ∣ ∣ - 5 [x] ∣ ∣ ∣ on [- 2, 2]$ is
(where $[x]$ denotes greatest integer function)

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Solution

The correct option is B 4
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 18 - x & - 2 \leq x < - 1 9 - x & - 1 \leq x < 0 x & 0 \leq x < 1 x + 3 & 1 \leq x < 2 8 & x = 2 \end{matrix}$

discontinuous at $x = - 1, 0, 1, 2$

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The number of points of discontinuity of f(x) where f(x)=∣∣∣∣∣|x+[x]|−3[x]∣∣−5[x]∣∣∣ on [−2,2] is (where [x] denotes greatest integer function)

The correct option is B 4f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩18−x−2≤x<−19−x−1≤x<0x0≤x<1x+31≤x<28x=2 discontinuous at x=−1, 0, 1, 2

The number of points of discontinuity of $f (x)$ where $f (x) = ∣ ∣ ∣ ∣ ∣ | x + [x] | - 3 [x] ∣ ∣ - 5 [x] ∣ ∣ ∣ on [- 2, 2]$ is
(where $[x]$ denotes greatest integer function)

The correct option is B 4
$f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 18 - x & - 2 \leq x < - 1 9 - x & - 1 \leq x < 0 x & 0 \leq x < 1 x + 3 & 1 \leq x < 2 8 & x = 2 \end{matrix}$

discontinuous at $x = - 1, 0, 1, 2$