Home
Class 11
MATHS
For the functionf(x)=[1/[[x]]] , where [...

For the function`f(x)=[1/[[x]]]` , where `[x]` denotes the greatest integer less than or equal to `x` , which of the following statements are true ?

A

The domain is (-infty, infty)

B

The range is`{0}cup{-1}cup{1}`

C

The range is (-infty,0)cup[1,infty)

D

The range is `{0}`cup`{1}`

Text Solution

Verified by Experts

The correct Answer is:
2,3
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos

  • FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x ), then

Let f(x)=sgn(cot^(-1)x)+tan((pi)/(2)[x]), where [x] is the greatest integer function less than or equal to x. Then which of the following alternatives is/are true?

The function f(x)=tan{pi[x-pi/2]}/(2+[x^2] , where [x] denotes the greatest integer le x, is

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

lim_(xrarr1([x]+[x]) , (where [.] denotes the greatest integer function )

Let f (x)= [x] where [x] denotes the greatest integer contained in x. Which one of the following is correct ?

if [x] denotes the greatest integer less than or equal to x then integral int_0^2x^2[x] dx equals

The function f(x)=(sec^(-1)x)/(sqrt(x-[x]), where [x] denotes the greatest integer less than or equal to x , is defined for all x in (a) R (b) R-{(-1,1)uu{n"|"n in Z}} (c) R-(0,1) (d) R-{n|n in N}

The function f(x)=(sec^(-1)x)/(sqrt(x-[x]), where [x] denotes the greatest integer less than or equal to x , is defined for all x in (a) R (b) R-{(-1,1)uu{n"|"n in Z}} (c) R-(0,1) (d) R-{n|n in N}

Draw the graph of y=[|x|] , where [.] denotes the greatest integer function.

PATHFINDER-FUNCTION-QUESTION BANK
  1. Let f[-2,2]rarrR be a continuous function such that f(x)assumes only i...

    Text Solution

    |

  2. Let f:NrarrR be such that f(1)=1and f(1)+2f(2)+3f(3)+......+nf(n)=n(n+...

    Text Solution

    |

  3. For the functionf(x)=[1/[[x]]] , where [x] denotes the greatest intege...

    Text Solution

    |

  4. Letf :(-pi/2,pi/2)rarrR be given by f(x)=(log)(secx+tan x))^3 Then

    Text Solution

    |

  5. If a in R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] deno...

    Text Solution

    |

  6. Let R be the set of all real numbers f:RrarrR be given by f(x)=3x^2+1....

    Text Solution

    |

  7. The function f(x)=x^2+bx+c, where b and c real constants , describes

    Text Solution

    |

  8. The range of the function y=(pi^2/16+x^2) is ?

    Text Solution

    |

  9. Letf(x)=2^100x+1,g(x)=3^100x+1 Then the set of real numbers x such tha...

    Text Solution

    |

  10. Which of the following real valued functions is/are not even functions...

    Text Solution

    |

  11. Letf:RrarrR be such that f is injective and f(x) f(y)=f(x+y) for all x...

    Text Solution

    |

  12. The function f[0,3]rarr[1,29], defined by f(x)=2x^3-15x^2+36x+1,is

    Text Solution

    |

  13. Let f(x)=ax^2+bx+c,g(x)=px^2+qx+r such that f(1)=g(1),f(2)=g(2)and f(3...

    Text Solution

    |

  14. The total number of infections (one-one into mappings) from {a1,a2,a3,...

    Text Solution

    |

  15. Let R be the set of real numbers and the functionsf:RrarrR and g:Rrarr...

    Text Solution

    |

  16. Letf(x)=x^2 and g(x)=sinx for all xIR then the set of all x satisfying...

    Text Solution

    |

  17. Letf:(0,1)rarrR be defined by f(x)=b-x/1-bx , where b is a constant su...

    Text Solution

    |

  18. The domain of the function f(x)=sin^-1((8(3)^(x-2))/(1-3^(2(x-1)))) is

    Text Solution

    |

  19. The domain of the function f(x)=1/sqrt(|x|-x) is

    Text Solution

    |

  20. The even function of the following is

    Text Solution

    |