Home
Class 12
MATHS
The function f(x)=[x]^2-[x^2] is discont...

The function `f(x)=[x]^2-[x^2]` is discontinuous at (where `[gamma]` is the greatest integer less than or equal to `gamma`), is discontinuous at

A

all integers

B

all integers except 0 and 1

C

all integers except 0

D

all integers except 1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Function f(x)=|x-2|-2|x-4| is discontinuous at

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

The function f(x)=[x^2] (where [y] is the greatest integer less than or equal to y ), is discontinuous at a. all integers b. all integers except 0 and 1 c. all integers except 0 d. all integers except 1

The function f(x)=x-[x]+cos x, where [x]= the greatest integer less than or equal to x is a

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

If f(x)=|x-1|-[x] (where [x] is greatest integer less than or equal to x ) then.

Show that the function defined by g(x)=x[x] is discontinuous at all integral points.Here [x] denotes the greatest integer less than or equal to x.

The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  2. If the functions f : R -> R and g : R -> R are such that f(x) is conti...

    Text Solution

    |

  3. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  4. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  5. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |

  6. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  7. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

    Text Solution

    |

  8. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

    Text Solution

    |

  9. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  10. Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...

    Text Solution

    |

  11. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  12. Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...

    Text Solution

    |

  13. Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...

    Text Solution

    |

  14. Let f(x) be continuous and differentiable function for all reals and f...

    Text Solution

    |

  15. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

    Text Solution

    |

  16. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x ge -1),(sin(pi(x+a))",","for...

    Text Solution

    |

  17. If both f(x) & g(x) are differentiable functions at x=x0then the fun...

    Text Solution

    |

  18. Number of points of non-differentiability of the function g(x) = [x^2...

    Text Solution

    |

  19. If f(x) = ({x}g(x))/({x}g(x)) is a periodic function with period (1)/(...

    Text Solution

    |

  20. If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists...

    Text Solution

    |