Home
Class 12
MATHS
Let f:DtoR, where D is the domain of f. ...

Let `f:DtoR`, where D is the domain of `f`. Find the inverse of `f` if it exists: `f(x)=ln(x+sqrt(1+x^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1):RtoR;f^(-1)=(e^(x)-e^(-x))/2`
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise MATCH THE COLUMN|5 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SCQ_TYPE|97 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SSP|55 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

Let f:D rarr R, where D is the domain off. Find the inverse of f, if it exists f(x)=1-2^(-x)

Let f:DtoR , where D is the domain of f . Find the inverse of f if it exists: f(x)=(4-(x-7)^(3))^(1//5)

Let f:DtoR , where D is the domain of f . Find the inverse of f if it exists: Let f:[0,3]to[1,13] is defined by f(x)=x^(2)+x+1 , then find f^(-1)(x) .

Let f:D rarr R where D is the domain of f then the inverse of f(x)=ln[x+sqrt(1+x^(2))] is

Domain of f(x)=log(1-x)+sqrt(x^(2)-1)

Find the domain and range of f(x)=[log(sin^(-1)sqrt(x^(2)+3x+2))]

Find the domain of f(x) = sqrt(x-1) .

Find the domain of the function f(x) defined by f(x)=sqrt(4-x)+(1)/(sqrt(x^(2)-1))

Find the domain of following function: f(x)=1/(log(2-x))+sqrt(x+1)

Find the domain and range of f(x) = sin{ln((sqrt(4-x^2))/(1-x))}

RESONANCE-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
  1. Let f : D -> R, where D is the domain off. Find the inverse of f, if ...

    Text Solution

    |

  2. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

    Text Solution

    |

  3. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

    Text Solution

    |

  4. Let f:DtoR, where D is the domain of f. Find the inverse of f if it ex...

    Text Solution

    |

  5. R rarr R be defined by f(x)=((e^(2x)-e^(-2x)))/2. is f(x) invertible. ...

    Text Solution

    |

  6. (a) If f(x)=-x|x|, then find f^(-1)(x) and hence find the number of so...

    Text Solution

    |

  7. If g is inverse of f(x) = x^3 + x + cosx, then find the value of g'(...

    Text Solution

    |

  8. If f(x)={((alpha-1)x,xepsilonQ^(c)),(-alpha^(2)x+alpha+3x-1,xepsilonQ)...

    Text Solution

    |

  9. Find the domain of each of the following function: f(x)=(sin^(-1)x)/x

    Text Solution

    |

  10. Find the domain of each of the following function: f(x)=sqrt(1-2x)+3si...

    Text Solution

    |

  11. Find the domain of each of the following function: f(x)=2^(sin^(-1)x)+...

    Text Solution

    |

  12. Find the range of each of the following f(x) = ln (sin^-1 x)

    Text Solution

    |

  13. Find the range of each of the following function: f(x)=sin^(-1)(sqrt...

    Text Solution

    |

  14. Find the range of each of the following function: f(x)=cos^(-1)(((x-...

    Text Solution

    |

  15. Find the simplified value of the following expression: sin[(pi)/3-si...

    Text Solution

    |

  16. Find the simplified value of the following expression: tan["cos"^(-1...

    Text Solution

    |

  17. Find the simplified value of the following expression: sin^(-1)[cos{...

    Text Solution

    |

  18. If sum(i=1)^(2n) sin^-1 xi = n pi then find the value of sum(i=1)^(...

    Text Solution

    |

  19. Solve the following inequality: cos^(-1)xgtcos^(-1)x^(2)

    Text Solution

    |

  20. Solve the following inequality: arc cot^(2)x-5 arc cotx+6gt0

    Text Solution

    |