Home
Class 11
MATHS
Find the domain of definition of the fun...

Find the domain of definition of the function `f(x)` given by `f(x)=1/(log_(10)(1-x))+sqrt(x+2)` .

Text Solution

Verified by Experts

`f(x)=1/(log_(10)​(1−x))​+sqrt((x+2))`
​ For this function to be defined,
`(1−x)gt0`,and `(x+2)ge0`
`xlt1`,and `xge−2`
Thus domain of f(x) is `x∈[−2,0)uu(0,1)`
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

Find the domain of definition of the function f(x) = sqrt(x^(2) - 25)

Find the domain of definition of the function f(x)=(x)/(sqrt(x-1))

The domain of definition of the function f(x)=sin^(-1)((x-3)/(2))-log_(10)(4-x) , is

Find the domain of definition of the function f(x) = sqrt(64 - x^(2)) .

The domain of definition of the function f(X)=x^((1)/(log_(10)x)) , is

The domain of the definition of the function f(x)=(1)/(4-x^(2))+log_(10)(x^(3)-x) is

The domain of definition of the function f(x) = sqrt(log_(x^(2)-1)) x is

Find the domain of the function f(x) = (1)/(log_(10) (1- x)) + sqrt(x + 3)

RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Find the domain of each of the following functions given by f(x)=1/(sq...

    Text Solution

    |

  2. Find the domain of definition of the following f(x) given by f(x)=log4...

    Text Solution

    |

  3. Find the domain of definition of the function f(x) given by f(x)=1/(lo...

    Text Solution

    |

  4. Find the range of each of the following functions: f(x)=|x-3| f(x)...

    Text Solution

    |

  5. Find the sum and product of identity function and the modulus function...

    Text Solution

    |

  6. If f(x)=1/(1-x) , show thatf[f{f(x)}]=xdot

    Text Solution

    |

  7. If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

    Text Solution

    |

  8. Find the domain of the real function f(x) defined by f(x)=sqrt((1-|x|)...

    Text Solution

    |

  9. If f is a real function satisfying f(x+1/x)=x^2+1/(x^2) for all x in ...

    Text Solution

    |

  10. Let f\ be a relation on the set NN of natural numbers defined by f={(...

    Text Solution

    |

  11. Let f be the subset of Z xxZ defined by f" "=" "{(a b ," "a" "+" "b)" ...

    Text Solution

    |

  12. Consider a rule f(x)=2x-3 associating elements of NN (set of natural n...

    Text Solution

    |

  13. Let A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->ZZ be given y f(x)=x^2-2x-3. F...

    Text Solution

    |

  14. Let A={1,2},\ B={3,6} and f: A->B given by f(x)=x^2+2\ and\ g: A->B gi...

    Text Solution

    |

  15. Let f : R - {2} rarr R be defined as f(x) = (x^2 - 4)/(x-2) and g: R...

    Text Solution

    |

  16. Let f: ZZ->ZZ\ a n d\ g: ZZ->ZZ\ be functions defined by f={(n , n^2)...

    Text Solution

    |

  17. Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){-5}

    Text Solution

    |

  18. Let f" "=" "{(1,1)," "(2," "3)," "(0, 1)," "(1," "3)} be a function fr...

    Text Solution

    |

  19. If f: RR->RR be defined as follows: f(x)={1,\ if\ x in QQ, -1,\ if\...

    Text Solution

    |

  20. If f: R->R be defined as follows: f(x)={1,\ if\ x in Q-1,\ if\ x !in ...

    Text Solution

    |