Home
Class 12
MATHS
The solution set for [x]{x}=1 (where {x...

The solution set for `[x]{x}=1` (where {x} and [x] are respectively, fractional part function and greatest integer function) is `R^+-(0,1)` (b) `r^+-{1}` `{m+1/m m in I-{0}}` `{m+1/m m in N-{1}}`

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x)=[sin{x}], where {} represents the fractional part function and [] represents the greatest integer function. A. -1 B. 0 C. 1 D. 0.5

Number of solutions of the equation [2x] - 3{2x} = 1 is (where [/] and {.} denote greatest integer and fractional part function respectively)

The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is where {dot} represents fractional part and [dot] represent greatest integral function). (a) R-I (b) R-[0,1] R-{Iuu(0,1)} (d) Iuu(0,1)

The range of the function f defined by f(x)=[1/(sin{x})] (where [.] and {dot}, respectively, denote the greatest integer and the fractional part functions) is

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 0) [(1+x)^(1/x)+e(x-1)]/x

Solve [cot^(-1) x] + [cos^(-1) x] =0 , where [.] denotes the greatest integer function

If M and m are the maximum and minimum values respectively of the function f(x)= x+ (1)/(x) , then the value of M - m is-

Integrate the functions 1/(x(logx)^(m)),xgt0,mne1

Solve (x-2)[x]={x}-1, (where [x]a n d{x} denote the greatest integer function less than or equal to x and the fractional part function, respectively).

lim_(xto0^(-)) (sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where ninN and [.] denotes the greatest integer function, equals

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes...

    Text Solution

    |

  2. If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetric ab...

    Text Solution

    |

  3. The solution set for [x]{x}=1 (where {x} and [x] are respectively, fr...

    Text Solution

    |

  4. Let f: RvecR be a continuous and differentiable function such that (f(...

    Text Solution

    |

  5. The possible values of a such that the equation x^2+2a x+a=sqrt(a^2+x-...

    Text Solution

    |

  6. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

    Text Solution

    |

  7. Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] den...

    Text Solution

    |

  8. If f(x+1)+f(x-1)=2f(x) and f(0)=0, then find f(n),n in N , is

    Text Solution

    |

  9. The range of the function f defined by f(x)=[1/(sin{x})] (where [.] ...

    Text Solution

    |

  10. If a, b be two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2 ...

    Text Solution

    |

  11. If f(x) = cos(loge x), then find the value of f(x)cdot f(y) - 1/2[f(x/...

    Text Solution

    |

  12. If x satisfies |x-1|+x-2|+|x-3| >= 6, then (a) 0 le x le 4 (b) x le ...

    Text Solution

    |

  13. Which of the following functions is periodic?

    Text Solution

    |

  14. The domain of definition of the function y=1/((log)(10)(1-x))+sqrt(x+...

    Text Solution

    |

  15. Let f(x)=sinx and g(x)=(log)e|x| If the ranges of the composition func...

    Text Solution

    |

  16. If a, b be two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2 ...

    Text Solution

    |

  17. Which of the following pairs of functions is/are identical? (a) f(x)=...

    Text Solution

    |

  18. Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer ...

    Text Solution

    |

  19. Which of the following is/are not functions ([.]) and {.} denote the ...

    Text Solution

    |

  20. Find the value of the x/9+y/4, when x=2, y=-3

    Text Solution

    |