Home
Class 12
MATHS
The domain of the function f(x)=sqrt(x^2...

The domain of the function `f(x)=sqrt(x^2-[x]^2)` , where `[x]` is the greatest integer less than or equal to `x ,` is (a) `R` (b) `[0,+oo)` (c) `(-oo,0)` (d) none of these

A

R

B

`[0,+oo)`

C

`(-oo,0]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2)-[x]^(2) ge 0 " or " x^(2) ge [x]^(2)`
This is true for all non-negative values of `x` and all negative integers `x`.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

let f(x)=(sin4pi[x])/(1+[x]^(2)) , where px] is the greatest integer less than or equal to x then

The value of int_(1)^(2)[x]dx , where [x] is the greatest integer less than or equal to x is

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

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

The domain of the function f(x)=log_e {sgn(9-x^2)}+sqrt([x]^3-4[x]) (where [] represents the greatest integer function is

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 R (b) R-{(-1,1)uu{n"|"n in Z}} R^+-(0,1) (d) R^+-{n|n in N}

IF the domain of the function f(x) =x^2 -6x +7 is (-oo , oo) then range of the function is

Find the domain of f(x)=sqrt(([x]-1))+sqrt((4-[x])) (where [ ] represents the greatest integer function).

("lim")_(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest integer function is equal to (a) 0 (b) -1 (c) not exist (d) none of these

Let f (x) = [x] , where [x] denotes the greater integer less than or equal to x. if a = sqrt(2011 ^2 +2012 ) then the value of f (a) is equal to

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

    Text Solution

    |

  2. The domain of f(x)=((log)2(x+3))/(x^2+3x+2) is (a)R-{-1,2} (b) (-2,oo...

    Text Solution

    |

  3. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  4. The domain of the function f(x)=(log)(3+x)(x^2-1) is (-3,-1)uu(1,oo) ...

    Text Solution

    |

  5. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

    Text Solution

    |

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

    Text Solution

    |

  7. If x^3f(x)=sqrt(1+cos2x)+|f(x)|, (-3pi)/4ltxlt(-pi) /2 and f(x)=(alpha...

    Text Solution

    |

  8. The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the gre...

    Text Solution

    |

  9. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |

  10. The domain of f(x)=cos^(-1)((2-|x|)/4)+[l log(3-x)]^1 is [-2,6] (b...

    Text Solution

    |

  11. The domain of the function f(x)=sqrt(log(1/(|sinx|))) R-{-pi,pi} (b)...

    Text Solution

    |

  12. Domain of definition of the function f(x) = log2 (-log(1/2) (1+x^(-4))...

    Text Solution

    |

  13. The number of real solutions of the (log)(0. 5)|x|=2|x| is (a) 1 (b) ...

    Text Solution

    |

  14. Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...

    Text Solution

    |

  15. The domain of the function f(x)=sqrt("In"((|x|-1))(x^(2)+4x+4)) is

    Text Solution

    |

  16. The domain of f(x)=1n(a x^3+(a+b)x^2+(b+c)x+c), where a >0,b^2-4a c=0,...

    Text Solution

    |

  17. The domain of the function f(x)=1/(sqrt(4x=|x^2-10 x+9})) is (7-sqrt(...

    Text Solution

    |

  18. The domain of the function f(x)=(1)/(sqrt(|cosx|+cosx)) is

    Text Solution

    |

  19. The exhaustive domain of the following function is f(x)=sqrt(x^(12)-x^...

    Text Solution

    |

  20. The number of integral values of x for which the function sqrt(sinx+co...

    Text Solution

    |