Home
Class 12
MATHS
The domain of the function f(x)=1/(sqrt(...

The domain of the function `f(x)=1/(sqrt(|x|-x))` is: (1) `(-oo,oo)` (2) `(0,oo` (3) `(-oo,""0)` (4) `(-oo,oo)"-"{0}`

A

`(-oo,oo) ~{0}`

B

`(-oo,oo)`

C

`(0,oo)`

D

(-oo,0)`

Text Solution

Verified by Experts

The correct Answer is:
D
The given function `f` is well defined only when `|x|-x gt 0`
`implies x lt 0`
` :. ` Required domain is `(-oo,0)`
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

The domain of the function f(x)=sqrt(log_((|x|-1))(x^2+4x+4)) is (a) (-3,-1)uu(1,2) (b) (-2,-1)uu(2,oo) (c) (-oo,-3)uu(-2,-1)uu(2,oo) (d)none of these

The domain of the function f(x)=sqrt(log(1/(|sinx|))) (a) R-{-pi,pi} (b) R-{npi|npiZ} (c) R-{2npi|n in z} (d) (-oo,oo)

The domain of the function f(x)=(sin^(-1)(3-x))/(I n(|x|-2)i s (a) [2,4] (b) (2,3)uu(3,4] (c) (0,1)uu(1,oo) (d) (-oo,-3)uu(2,oo)

The function f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo) is

The domain of the function f(x)=sqrt(10-sqrt(x^4-21 x^2)) is a. [5,oo) b. [-sqrt(21),sqrt(21)] c. [-5,-sqrt(21)]uu[sqrt(21),5]uu{0] d. (-oo,-5] U [5,oo)

The value of int_0^oo (dx)/(1+x^4) is

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

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

Solution set of the inequality 1/(2^x-1)>1/(1-2^(x-1)) is 1,oo) (b) 0,(log)_2(4/3) (c) (-1,oo) (0,(log)_2(4/3)uu(1,oo)

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)

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If 4^x-2^(x+2)+5+||b-1|-3|-siny|, x , y , b in R , then the possible ...

    Text Solution

    |

  2. If f: NvecN ,a n dx2> x1f(x2)>f(x1)AAx1,x2 in Na n df(f(n))=2nAAn in ...

    Text Solution

    |

  3. The number of integral values of a for which f(x)="log"((log)(1/3)((lo...

    Text Solution

    |

  4. Let f(x)=sin^(23)x-cos^(22)xa n dg(x)=1+1/2tan^(-1)|x| . Then the numb...

    Text Solution

    |

  5. Suppose that f(x) is a function of the form f(x)=(ax^(8)+bx^(6)+cx^...

    Text Solution

    |

  6. The function f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo) is

    Text Solution

    |

  7. Period of the function f(x)=sin((x)/(2))cos [(x)/(2)]-cos((x)/(2))s...

    Text Solution

    |

  8. If the interval x satisfying the equation |x| +|-x|=(log(3)(x-2))/(|...

    Text Solution

    |

  9. If f: RvecNuu{0}, where f (area of triangle joining points P(5,0),Q(8,...

    Text Solution

    |

  10. For real x, let f(x)""=""x^3+""5x""+""1 , then (1) f is oneone but not...

    Text Solution

    |

  11. Let f:[-1,oo] in [-1,oo] be a function given f(x)=(x+1)^(2)-1, x ge -1...

    Text Solution

    |

  12. Consider the following relations: R = {(x, y) | x, y are real numbers ...

    Text Solution

    |

  13. Let R be the set of real numbers Statement-1: A = {(x,y) in R xx R :...

    Text Solution

    |

  14. The domain of the function f(x)=1/(sqrt(|x|-x)) is: (1) (-oo,oo) (2...

    Text Solution

    |

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

    Text Solution

    |

  16. If f(x)+2f(1/x)=3x , x!=0, and S={x in R :f(x)=f(-x)} ; then S: (1) i...

    Text Solution

    |

  17. The function f:R->[-1/2,1/2] defined as f(x)=x/(1+x^2) is

    Text Solution

    |

  18. Let a,b, c in R. " If " f(x)=ax^(2)+bx+c is such that a+b+c=3 and f(x+...

    Text Solution

    |

  19. Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then f(...

    Text Solution

    |

  20. Let f(x)=sin[pi/6sin(pi/2sinx)] for all x in RR then prove that Range...

    Text Solution

    |