Home
Class 12
MATHS
Consider a function defined in [-2,2] ...

Consider a function defined in `[-2,2]`
`f (x)={{:({x}, -2 lle x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):},` where {.} denotes the fractional part function.
The total number of points of discontinuity of `f (x)` for `x in[-2,2]` is:

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|1 Videos

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|23 Videos

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos

  • COMPOUND ANGLES

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|31 Videos

  • DETERMINANTS

    VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

Similar Questions

Explore conceptually related problems

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The number of points for x in [-2,2] where f (x) is non-differentiable is:

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt x le 3):}, then

Let a function f(x) be defined in [-2, 2] as f(x) = {{:({x}",",, -2 le xlt -1), (|"sgn "x|",",,-1le x le 1),({-x}",",, 1 lt xle 2):} where {x} and sgn x denote fractional part and signum functions, respectively. Then find the area bounded by the graph of f(x) an the x-axis.

Consider the function f(x) = [{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

If f(x)= {(|1-4x^2|,; 0 lt= x lt 1), ([x^2-2x],; 1 lt= x lt 2):} , where [.] denotes the greatest integer function, then f(x) is

If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x le 2):} , then f is

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then

Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x le 2):} and g(x)={([x]",",-pi le x lt 0),(sinx",",0le x le pi):} where [.] denotes the greatest integer function. The number of integral points in the range of g(f(x)) is

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Define: f (x) =|x^(2)-4x +3| ln x+2 (x-2)^(1//3) , x gt 0 h (x)= {{:...

    Text Solution

    |

  2. Define: f (x) =|x^(2)-4x +3| ln x+2 (x-2)^(1//3) , x gt 0 h (x)= {{...

    Text Solution

    |

  3. Consider a function defined in [-2,2] f (x)={{:({x}, -2 lle x lt -1)...

    Text Solution

    |

  4. Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),...

    Text Solution

    |

  5. Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ ...

    Text Solution

    |

  6. Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ ...

    Text Solution

    |

  7. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

    Text Solution

    |

  8. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

    Text Solution

    |

  9. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

    Text Solution

    |

  10. Let f :R to R be a continous and differentiable function such that f (...

    Text Solution

    |

  11. Let f :R to R be a continous and differentiable function such that f (...

    Text Solution

    |

  12. Let f :R to R be a continous and differentiable function such that f (...

    Text Solution

    |

  13. f(x)=(cos^2x)/(1+cosx+cos^2x) and g(x)=ktanx+(1-k)sinx-x, where k in R...

    Text Solution

    |

  14. f(x)=(cos^2x)/(1+cosx+cos^2x) and g(x)=ktanx+(1-k)sinx-x, where k in R...

    Text Solution

    |

  15. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

    Text Solution

    |

  16. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

    Text Solution

    |

  17. f (x) = lim (x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +...

    Text Solution

    |

  18. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

    Text Solution

    |

  19. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

    Text Solution

    |

  20. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

    Text Solution

    |