Home
Class 12
MATHS
Let f:[-1,oo]vec[-1,) is given by f(x)=(...

Let `f:[-1,oo]vec[-1,)` is given by `f(x)=(x+1)^2-1,xgeq-1.` Show that `f` is invertible. Also, find the set `S={x :f(x)=f^(-1)(x)}dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

Let f:[-1,1] to R_(f) be a function defined by f(x)=(x)/(x+2) . Show that f is invertible.

Show that f: R-{-1}->R-{1} given by f(x)=x/(x+1) is invertible. Also, find f^(-1) .

Let f:[-1,oo] in [-1,oo] be a function given f(x)=(x+1)^(2)-1, x ge -1 Statement-1: The set [x:f(x)=f^(-1)(x)]={0,1} Statement-2: f is a bijection.

Consider f: R rarr [-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=((sqrt(y+6)-1)/3)dot

Consider f: R_+->[-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=(((sqrt(y+6))-1)/3)

Consider f\ : R_+vec[4,oo) given by f(x)=x^2+4 . Show that f is invertible with the inverse f^(-1) of f given by f^(-1)(y)=sqrt(y-4),\ where R_+ is the set of all non-negative real numbers.

If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is invertible, find f^(-1)

If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is invertible, find f^(-1)

Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and hence find f^(-1) .

Let f: R-{-1}->R-{1} be given by f(x)=x/(x+1) . Write f^(-1)(x) .

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

    Text Solution

    |

  2. If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invert...

    Text Solution

    |

  3. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

    Text Solution

    |

  4. Let A={x in R|-1lt=xlt=1} and let f: A->A ,\ g: A->A be two functions...

    Text Solution

    |

  5. Let f be a function from R to R such that f(x)=cos(x+2) . Is f inverti...

    Text Solution

    |

  6. If A={1,\ 2,\ 3,\ 4} and B={a ,\ b ,\ c ,\ d} . Define any four bij...

    Text Solution

    |

  7. Let A and B be two sets each with a finite number of elements. Assume ...

    Text Solution

    |

  8. If f: AvecA ,g: Avec are two bijections, then prove that fog is an inj...

    Text Solution

    |

  9. If f: A->A ,\ \ g: A->A are two bijections, then prove that fog is an ...

    Text Solution

    |

  10. Which one of the following graphs represent a function? (FIGURE)

    Text Solution

    |

  11. Which one of the following graphs represent a one-one function? (FI...

    Text Solution

    |

  12. Let A={1,\ 2} and B={a ,\ b} be two sets. Write total number of one-...

    Text Solution

    |

  13. Write total number of one-one functions from set A={1,\ 2,\ 3,\ 4} ...

    Text Solution

    |

  14. If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

    Text Solution

    |

  15. If f: C->C is defined by f(x)=x^2 , write f^(-1)(-4) . Here, C denotes...

    Text Solution

    |

  16. If f: R->R is given by f(x)=x^3 , write f^(-1)(1) .

    Text Solution

    |

  17. Let C denote the set of all complex numbers. A function f: C->C is def...

    Text Solution

    |

  18. Let f be a function from C (set of all complex numbers) to itself g...

    Text Solution

    |

  19. Let f: R->R be defined by f(x)=x^4 , write f^(-1)(1) .

    Text Solution

    |

  20. Find the derivative of f(x)=x^4

    Text Solution

    |