Home
Class 12
MATHS
The function, f(x)=[|x|]-|[x]| where [] ...

The function, `f(x)=[|x|]-|[x]|` where [] denotes greatest integer function:

A

is continuous for all positive integers

B

is discontinuous for all non-positive integers

C

has finite number of elements in its range

D

is such that its graph does not lie above the X-axis

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

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

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|50 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

The range of the function f(x)=2+x-[x-3] is, (where [.] denotes greatest integer function):

The function f(x)=[x], where [x] denotes the greatest integer function,is continuous at

The function f(x)=x-[x], where | denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only ( continuous at non- integer points only (d) differentiable everywhere

Find the range of the following function: f(x)=ln(x-[x]), where [.] denotes the greatest integer function

The period of the function f(x)=sin(x+3-[x+3]) where [] denotes the greatest integer function

Let us consider a function f(x)=sin[x] where [x] denotes the greatest integer function.Then

Consider the function f(x) = {x+2} [cos 2x] (where [.] denotes greatest integer function & {.} denotes fractional part function.)

Find the domain and range of the following function: f(x)=log_([x-1])sinx, where [ ] denotes greatest integer function.

If f(x)=[2x], where [.] denotes the greatest integer function,then

The domain of function f(x)=sqrt(log_([x])|x|) (where denotes greatest integer function),is

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)
  1. If f(x) = |x+1|(|x|+|x-1|), then at what points the function is/are no...

    Text Solution

    |

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

    Text Solution

    |

  3. If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...

    Text Solution

    |

  4. Q. Let f(x)=cos x $ H(x)=[min [f(t) 0<=t<=x for 0<=x<=p...

    Text Solution

    |

  5. If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then

    Text Solution

    |

  6. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

    Text Solution

    |

  7. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

    Text Solution

    |

  8. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

    Text Solution

    |

  9. The function, f(x)=[|x|]-|[x]| where [] denotes greatest integer funct...

    Text Solution

    |

  10. The function f(x)=sqrt(1-sqrt(1-x^2))

    Text Solution

    |

  11. Consider the function f(x) = |x^(3) + 1|. Then,

    Text Solution

    |

  12. f is a continous function in [a, b]; g is a continuous function in [b,...

    Text Solution

    |

  13. Which of the following function(s) has/have the same range ?

    Text Solution

    |

  14. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

    Text Solution

    |

  15. Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is conti...

    Text Solution

    |

  16. A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0)...

    Text Solution

    |

  17. Let f(x) = int(-2)^(x)|t + 1|dt, then

    Text Solution

    |

  18. A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...

    Text Solution

    |

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

    Text Solution

    |

  20. If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x...

    Text Solution

    |