Home
Class 12
MATHS
Find the domain and range of f(f)=log{x}...

Find the domain and range of `f(f)=log{x},w h e r e{}` represents the fractional part function).

Text Solution

Verified by Experts

We know that `o le {x} lt 1 AA x in R.`
Now, when `{x} =0, log{x}` is not defined. So, x cannot be an integer. Hence, the domain is `R-I`.
Now, for `0 lt {x} lt 1, -oo lt log {x} lt 0. ` So, range is `(-oo,0).`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the domain and range of f(f)=log{x}, where {} represents the fractional part function).

Domain of function f(x)=ln(x), where {} represents fractional part function.

Find the range of f(x)=x-{x} , where {.} is the fractional part function.

Find the domain and range of f(x)=sin^(-1)[x] wher [] represents the greatest function).

f(x) = cos^(-1){ log[sqrt[x^3+1]]} , find the domain and range of f(x) (where [ * ] denotes the greatest integer function).

If domain of f(x) is (-oo,0], then domain of f(6{x}^(2)-5(x)+1) is (where {.} represents fractional part function)

Domain of the function f(x)=log_(e)cos^(-1){sqrt(x)}, where {.} represents fractional part function

Find the range of f(x)=cos(log_(e){x})

Find the domain and range of f(x)="sin"^(-1)(x-[x]), where [.] represents the greatest integer function.

The domain of function f(x)=ln(ln((x)/({x}))) is (where { ) denotes the fractional part function)

CENGAGE-RELATIONS AND FUNCTIONS-Solved Examples And Exercises
  1. Find the domain and range of f(f)=log{x},w h e r e{} represents the fr...

    Text Solution

    |

  2. Find the inverse of the function: f:(-oo,1] rarr [1/2,oo],w h e r ef(...

    Text Solution

    |

  3. Find the value of x for which function are identical. f(x)=xa n dg(x)=...

    Text Solution

    |

  4. Find the value of x for which function are identical. f(x)=cosxa n dg(...

    Text Solution

    |

  5. Find the value of x for which function are identical. f(x)=(sqrt(9-x^2...

    Text Solution

    |

  6. Find the inverse of the function: f: R rarr (-oo,1)gi v e nb yf(x)=1-...

    Text Solution

    |

  7. f:(2,3)vec(0,1)d efin e db yf(x)=x-[x],w h e r e[dot] represents the g...

    Text Solution

    |

  8. Find the inverse of the function: f(x)={x^3-1, ,x<2x^2+3,xgeq2

    Text Solution

    |

  9. Find the inverse of the function: f:[-1,1]rarr[-1,1]defined byf(x)=x|...

    Text Solution

    |

  10. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  11. Let f(x)=(9^x)/(9^x+3) . Show f(x)+f(1-x)=1 and, hence, evaluate. f(1/...

    Text Solution

    |

  12. If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

    Text Solution

    |

  13. Let g(x) be a function such that g(a+b)=g(a)dotg(b)AAa , b in Rdot If...

    Text Solution

    |

  14. Find the value of x for which function are identical. f(x)=tan^(-1)x+t...

    Text Solution

    |

  15. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

    Text Solution

    |

  16. Plot y=|x|,y=|x-2|, and y=|x+2|

    Text Solution

    |

  17. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

    Text Solution

    |

  18. If for all real values of ua n dv ,2f(u)cosv=(u+v)+f(u-v), prove that ...

    Text Solution

    |

  19. If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= ...

    Text Solution

    |

  20. If f: X rarr[1,oo) is a function defined as f(x)=1+3x^3, find the su...

    Text Solution

    |

  21. Find the period (if periodic) of the following function ([.] denotes ...

    Text Solution

    |