Home
Class 11
MATHS
If f:RR rarr RR is defined by f(x)=x-[x]...

If `f:RR rarr RR` is defined by `f(x)=x-[x] -(1)/(2)" for "x in RR`, where `[x]` is the greatest integer not exceeding x, then `{x in RR : f(x)=(1)/(2)}=`

A

Z, the set of all integers

B

N, the set of all natural numbers

C

`phi`, the empty set

D

R

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|50 Videos

  • FUNCTIONS

    AAKASH SERIES|Exercise EXERCISE -I|53 Videos

  • ERRORS AND APPROXIMATIONS

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTION|15 Videos

  • HEIGHTS AND DISTANCES

    AAKASH SERIES|Exercise PRACTICE SHEET Exercise-I (Level-II) (Straight Objective Type Questions)|13 Videos

Similar Questions

Explore conceptually related problems

If f: R rarr R is defined by f(x)= x-[x]- 1/2 for x in R , where [x] is the greatest integer not exceeding x, then {x in R : f(x) + 1/2}=

If f:RR rarr RR is defined by f(x)=[(x)/(2)] for x in RR , where [y] denotes the greatest integer not exceeding, y then {f(x):|x| lt 71}=

If f: R rarr R is defined by f(x)= [2x]-2[x] for x in R , where [x] is the greatest integer not exceeding x, then the range of f is

If f : R to R is defined by f(x) = [2x]-2[x] for x in R , where [x] is the greatest integer not exceeding x, then the range of f is:

If f: R rarr R is defined by f(x)= [x/5] for x in R , where [y] denotes the greatest integer not exceding y, then {f(x):|x| lt 71}=

If f: R rarr R and g:R rarr R are defined by f(x)=x - [x] and g(x)=[x] for x in R , where [x] is the greatest integer not exceeding x , then for every x in R, f(g(x))=

If f:R rarr R is defined by f(x)=[2x]-2[x] for x in R , then the range of f is (Here [x] denotes the greatest integer not exceding x)

AAKASH SERIES-FUNCTIONS -EXERCISE -II
  1. If g[f(x)]=|sinx|, f[g(x)]=(sinsqrtx)^(2) then

    Text Solution

    |

  2. If f(x) = cos|e^(2)| x + cos[-e^(2)]x where [x] stands for greatest in...

    Text Solution

    |

  3. If f:RR rarr RR is defined by f(x)=x-[x] -(1)/(2)" for "x in RR, where...

    Text Solution

    |

  4. Let g(x) =1+x-[x] and f(x) ={{:(-1, if, x lt 0),(0, if, x=0),(1, if, x...

    Text Solution

    |

  5. If f: R to R and g: R to R are defined by f(x) =x-[x] and g(x) =[x] A...

    Text Solution

    |

  6. If f(x)=[x], g(x)=x-[x] then which of the following functions is the z...

    Text Solution

    |

  7. If f : R to R and g: R to R are given by f(x) =|x| and g(x) =[x] for e...

    Text Solution

    |

  8. f(x) = {{:([x], if, -3 lt x le -1),(|x|, if, -1 lt x lt 1),(|[-x]|, if...

    Text Solution

    |

  9. If f(x) is a polynomial fin x( gt0) satisfying the equation f(x)+f(1//...

    Text Solution

    |

  10. If f(x) is a polynomial function such that f(x)f((1)/(x))=f(x)+f((1)/(...

    Text Solution

    |

  11. If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, f...

    Text Solution

    |

  12. If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

    Text Solution

    |

  13. f: R to R is given by: f(x)= a^(x)/(a^(x) + sqrt(a)) AA x in R, then ...

    Text Solution

    |

  14. If f(x) =((x-a)(x-b))/x and (f(x))/((x-y)(x-z))+ (f(y))/((x-z)(y-z)) +...

    Text Solution

    |

  15. If 2f(x) -3f(1/x)=x^(2), x ne 0, then f(2)=

    Text Solution

    |

  16. If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) " for " x=3, 4, 5, ……...

    Text Solution

    |

  17. If f(x+y,x-y) =xy, then the arithmetic mean of f(x,y) and f(y,-x) is

    Text Solution

    |

  18. Assertion (A) P:f(x) =logx^(3) and g(x) =3 log x are equal functions ...

    Text Solution

    |

  19. Let f(x) =px^(2) + qx^(4) +r. Then for f to be on even function:

    Text Solution

    |

  20. If f(x) =ax^(5) + bx^(3) + cx +d is an odd function, then d=

    Text Solution

    |