Let [ t ] denote the greatest integer ≤ t. The number of points where the function f ( x )=[ x ]| x 2-1|+ sin ((π/[ x ]+3))-[ x +1], x ∈(-2,2) is not continuous is

Question

Let [ t ] denote the greatest integer ≤ t. The number of points where the function f ( x )=[ x ]| x 2-1|+ sin ((π/[ x ]+3))-[ x +1], x ∈(-2,2) is not continuous is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x)=[x]|x2-1|+ sin (π/[x+3])-[x+1] f(x)= begincases3-2 x2, -2< x< -1 x2, -1 ≤ x< 0 (√3/2)+1 0 ≤ x<1 x2+1+(1/√2), 1 ≤ x< 2 endcases discontinuous at x=0,1

Q. Let $[t]$ denote the greatest integer $\leq t$ . The number of points where the function
$f (x) = [x] ∣ ∣ x^{2} - 1 ∣ ∣ + sin (\frac{π}{[ x ] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is

$f (x) = [x] ∣ ∣ x^{2} - 1 ∣ ∣ + sin \frac{π}{[ x + 3 ]} - [x + 1]$
$f (x) = ⎩ ⎨ ⎧ 3 - 2 x^{2}, x^{2}, \frac{3}{2} + 1 x^{2} + 1 + \frac{1}{2}, - 2 < x < - 1 - 1 \leq x < 0 0 \leq x < 1 1 \leq x < 2$
discontinuous at $x = 0, 1$

Q. Let [t] denote the greatest integer ≤t. The number of points where the function f(x)=[x]∣∣​x2−1∣∣​+sin([x]+3π​)−[x+1],x∈(−2,2) is not continuous is

f(x)=[x]∣∣​x2−1∣∣​+sin[x+3]π​−[x+1] f(x)=⎩⎨⎧​3−2x2,x2,23​​+1x2+1+2​1​,​−2<x<−1−1≤x<00≤x<11≤x<2​ discontinuous at x=0,1

Q. Let $[t]$ denote the greatest integer $\leq t$ . The number of points where the function
$f (x) = [x] ∣ ∣ x^{2} - 1 ∣ ∣ + sin (\frac{π}{[ x ] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is

$f (x) = [x] ∣ ∣ x^{2} - 1 ∣ ∣ + sin \frac{π}{[ x + 3 ]} - [x + 1]$
$f (x) = ⎩ ⎨ ⎧ 3 - 2 x^{2}, x^{2}, \frac{3}{2} + 1 x^{2} + 1 + \frac{1}{2}, - 2 < x < - 1 - 1 \leq x < 0 0 \leq x < 1 1 \leq x < 2$
discontinuous at $x = 0, 1$