Let f(x)=x ⋅[(x/2)], for -10

Question

Let f(x)=x ⋅[(x/2)], for -10< x< 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x ∈(-10,10) (x/2) ∈(-5,5) arrow 9 integers check continuity at x=0 f (0)=0 f (0+)=0 f (0-=0 continuous at x = 0 function will be distcontinuous when (x/2)=± 4,± 3,± 2,± 1 8 points of discontinuity

Q. Let $f (x) = x \cdot [\frac{x}{2}],$ for $- 10 < x < 10,$ where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to______.

$x \in (- 10, 10)$
$\frac{x}{2} \in (- 5, 5) \to 9$ integers
check continuity at $x = 0$
$f (0) = 0}, f (0^{+}) = 0}, f (0^{-} = 0}$ continuous at x = 0
function will be distcontinuous when
$\frac{x}{2} = \pm 4, \pm 3, \pm 2, \pm 1$
8 points of discontinuity

Q. Let f(x)=x⋅[2x​], for −10<x<10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to______.

x∈(−10,10) 2x​∈(−5,5)→9 integers check continuity at x=0 f(0)=0},f(0+)=0},f(0−=0} continuous at x = 0 function will be distcontinuous when 2x​=±4,±3,±2,±1 8 points of discontinuity

Q. Let $f (x) = x \cdot [\frac{x}{2}],$ for $- 10 < x < 10,$ where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to______.

$x \in (- 10, 10)$
$\frac{x}{2} \in (- 5, 5) \to 9$ integers
check continuity at $x = 0$
$f (0) = 0}, f (0^{+}) = 0}, f (0^{-} = 0}$ continuous at x = 0
function will be distcontinuous when
$\frac{x}{2} = \pm 4, \pm 3, \pm 2, \pm 1$
8 points of discontinuity