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)=(4-(x-7)^(3))^(1//5)`

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1):RtoR;f^(-1)=7+(4-x^(5))^(1//3)`

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

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: 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

Let f:vec N be a function defined as f(x)=9x^(2)+6x-5. Show that f:Nvec S where S is the range of f, is invertible.Find the inverse of f and hence f^(-1)(43) and f^(-1)(163)

Let f : R to R : f (x) =(3-x^(3))^(1//3). Find f o f

If f(x)=x^(2)-x+1 , then find the inverse of the f (x)

If f(x)=|sin x| then domain of for the existence of inverse of

Let f:N rarr N, where f(x)=x+(-1)^(x-1), then the inverse of is.

Find the domain of f(x) = (5)/(x-3)

RESONANCE-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
  1. Find the fundamental period of the following function: f(x)=sec^(3)x...

    Text Solution

    |

  2. Let f : D -> R, where D is the domain off. Find the inverse of f, if ...

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |