Home
Class 11
MATHS
Write the domain and range of function f...

Write the domain and range of function `f(x)` given by `f(x)=1/(sqrt(x-[x]))`

Text Solution

Verified by Experts

`f(x)=frac{1}{sqrt(x-abs(X))}`
`x-abs(x)={(x,-,x,=,0, ifx>=0),(x,+,x,=,2x, if x<0):}`
`x-abs(x)=<=0` for all `x`
`frac{1}{sqrt(x-abs(X))}` does not take any real value for any `x in R`
Hence, domain (`f`)=`phi` and range (`f`)=`phi`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos
  • GEOMETRIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|255 Videos

Similar Questions

Explore conceptually related problems

Write the domain and range of function f(x) given by f(x)=sqrt([x]-x) .

Write the domain and range of the function f(x)=[x]

Find the domain and range of the function f(x) given by f(x)=(x-2)/(3-x)

Write the domain and range of f(x)=sqrt(2x-1)

Find the domain and range of the function f given by f(x) = x^2/(1-x^2)

Write the domain and the range of the function, f(x)=-|x| .

Find the domain and range of the function f(x) = x/(2 - 3x)

Find the domain and range of the function f(x) = sqrt(x-1)

Find the domain of the function f given by f(x)=(1)/(sqrt([x]^(2)-[x]-6))

Find the domain and range of the function f(x) = (x)/(1 + x^(2))

RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. If f(x)=4x-x^2, x in R , then write the value of f(a+1)-f(a-1)dot

    Text Solution

    |

  2. If f,\ g,\ h are real functions given by f(x)=x^2,g\ (x)=tanx\ a n d\ ...

    Text Solution

    |

  3. Write the domain and range of function f(x) given by f(x)=1/(sqrt(x-[x...

    Text Solution

    |

  4. Write of the domain and range of f(x)=sqrt(x-[x])dot

    Text Solution

    |

  5. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x).

    Text Solution

    |

  6. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

    Text Solution

    |

  7. Find the values of x for which the functions f(x)=3x^2-1 and g(x)=3+x ...

    Text Solution

    |

  8. If f(x)="cos"((log)e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value ...

    Text Solution

    |

  9. Let f(x)=|x-1|dot Then (a)f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c)f(...

    Text Solution

    |

  10. If A={1,2,3},\ B={x , y} , then the number of functions that can be de...

    Text Solution

    |

  11. If x!=1\ a n d\ f(x)=(x+1)/(x-1) is a real function, then f(f(f(2))) ...

    Text Solution

    |

  12. If f: R->R : x!=0,\ -4lt=xlt=4 and f: A->A be defined by f(x)=(|x|)/x ...

    Text Solution

    |

  13. If f: RrarrR and g: RrarrR are defined by f(x)=2x+3a n dg(x)=x^2+7, th...

    Text Solution

    |

  14. If f: [-2, 2] -> R is defined by f(x)={-1,for -2<=x<=0 , then x...

    Text Solution

    |

  15. If f(x)=64x^3+1/x^3 and alpha,beta are the roots of 4x+1/x=3. Then,f(a...

    Text Solution

    |

  16. The domain of the function f(x)=sqrt(2-2x-x^2) is [-sqrt(3),\ sqrt(3)...

    Text Solution

    |

  17. The domain of the function f(x)=sqrt[((x+1)(x-3))/(x-2)] is [-1,2)uu[3...

    Text Solution

    |

  18. The domain of the function f(x)=sqrt(((x+1)(x-3))/(x-2)) is [-1,2)uu[3...

    Text Solution

    |

  19. The domain of definition of the function f(x)=sqrt(x-1)+sqrt(3-x) is [...

    Text Solution

    |

  20. The domain of definition of the function f(x)=sqrt((x-2)/(x+2))+sqrt((...

    Text Solution

    |