Home
Class 12
MATHS
Let f(x)=sqrt(|x|-|x+)(w h e r e{dot} de...

Let `f(x)=sqrt(|x|-|x+)(w h e r e{dot}` denotes the fractional part of `(x)a n dX , Y` are its domain and range, respectively). Then `x in (-oo,1/2)a n dY in (1/2,oo)` `x in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo)` `X in (-oo,-1/2)uu[0,oo)a n dY in (1/2,oo)`

A

`f:X rarr Y:y=f(x)` is one-one function

B

`X in (-infty,-1/2] cup [0,infty) " and " Y in [1/2,infty)`

C

`X in (-infty,-1/2] cup [0,infty) " and " Y in [0,infty)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|22 Videos

  • FUNCTIONS

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

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 12|4 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional part of (x) ) is equal to (a)does not exist (b) 1 (c) oo (d) 1/2

Solution set of the inequation, (x^2-5x+6)/(x^2+x+1)<0 is x in (-oo,2) (b) x in (2,3) x in (-oo,2)uu(3,oo) (d) x in (3,oo)

If |x+2|lt=9 then x in (-7, 11) b. x in [-11 ,7] c. x in (-oo,7)uu(11 ,oo) d. x in (-oo,-7)uu[11 ,oo)

If |x-1|>5, then a. x in (-4,6) b. x in [-4,6] c. x in (-oo,-4)uu(6,oo) d. x in (-oo,-4)uu[6,oo)

Solution set of the inequation (x^2+4x+4)/(2x^2-x-1)>0, is x in (-oo,-2)uu(-2,1) x in (-oo,-2)uu(-2,-1/2)uu(1,oo) x in (-oo,-2)uu(-1/2,1)uu(1,oo) x in (-oo,1)

If x\ a n d\ a are real numbers such that a >0 and |x|> a , then (a) x in (-a ,oo) b. x in [-oo, a) c. x in (-a , a) d . x in (-oo,-a)U(a ,oo)

Let f(x)=[x]cos ((pi)/([x+2])) where [ ] denotes the greatest integer function. Then, the domain of f is (a) x epsilon R, x not an integer (b) x epsilon (-oo, -2)uu[-1,oo) (c) x epsilon R, x!=-2 (d) x epsilon (-oo,-1]

The domain of f(x)="log"|logx|i s (0,oo) (b) (1,oo) (c) (0,1)uu(1,oo) (d) (-oo,1)

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

ARIHANT MATHS ENGLISH-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. The range of values of a so that all the roots of the equations 2x^(3)...

    Text Solution

    |

  2. If f(x) is continuous such that abs(f(x)) le 1, forall x in R " and " ...

    Text Solution

    |

  3. Let f(x)=sqrt(|x|-|x+)(w h e r e{dot} denotes the fractional part of (...

    Text Solution

    |

  4. If the graphs of the functionsy= log (e)x and y = ax intersect at exac...

    Text Solution

    |

  5. A quadratic polynomial maps from [-2,3] onto [0,3] and touches X-axis ...

    Text Solution

    |

  6. The range of the function y=sqrt(2{x}-{x}^2-3/4) (where, denotes the f...

    Text Solution

    |

  7. Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x...

    Text Solution

    |

  8. Number of solutions of the equation, [y+[y]]=2cosx is: (where y=1//3)[...

    Text Solution

    |

  9. If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x), then period of f(x)...

    Text Solution

    |

  10. If x and alpha are real, then the inequation log(2)x+log(x)2+2cos al...

    Text Solution

    |

  11. The range of values of ‘a' such that (1/2)^|x|= x² - a is satisfied f...

    Text Solution

    |

  12. Let f:R rarr R be a function defined by f(x)={abs(cosx)}, where {x} re...

    Text Solution

    |

  13. The domain of the function f(x)=sqrt(log(sinx+cosx)(abs(cosx)+cosx))...

    Text Solution

    |

  14. If f(x)=(x^(2)+2alphax+alpha^(2)-1)^(1//4) has its domain and range su...

    Text Solution

    |

  15. If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is - (a)f is one-...

    Text Solution

    |

  16. The expression x^2-4px+q^2> 0 for all real x and also r^2+ p^2 < qr t...

    Text Solution

    |

  17. Let f(x)=(x^(4)-lambdax^(3)-3x^(2)+3lambdax)/(x-lambda). If range of f...

    Text Solution

    |

  18. Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C(0)a^(n-1)-""...

    Text Solution

    |

  19. The area bounded by f(x)=sin^(-1)(sinx) and g(x)=pi/2-sqrt(pi^(2)/2-...

    Text Solution

    |

  20. If f.R rarr R,f(x)=(x^(2)+bx+1)/(x^(2)+2x+b),(b gt 1) " and " f(x), 1/...

    Text Solution

    |