Home
Class 12
MATHS
Find f^(-1) if it exists: f: A->B where ...

Find `f^(-1)` if it exists: `f: A->B` where `A={1,\ 3,\ 5,\ 7,\ 9};` `B=` `{0,\ 1,\ 9,\ 25 ,\ 49 ,\ 81}` and `f(x)=x^2` .

Text Solution

Verified by Experts

`A={1,3,5,7,9}; B={0,1,9,25,49,81} and f(x)=x^2`

`f:A rightarrowB`

` Rightarrow f(x)=x^2`

` Rightarrow So, f={(1,1),(3,9),(5,25),(7,49),(9,81)} `

We know ,distnict elements in A has distnict images in B.

So , f is one-one.

...
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

Find f^(-1) if it exists: f: A->B where A={0,\ -1,\ -3,\ 2}; B= {-9,\ -3,\ 0,\ 6} and f(x)=3x .

If A=[(3,1),(-1,2)] , then find f (A), where f(x)=x^(2)-5x+7 .

If f(x)=3x^4-5x^2+9, find f(x-1) .

Let A = {-1, 1, 2, 3, 5}, B = {1, 4, 9, 11, 25, 29}. The rule f given by f(x) = x^(2) is a mapping from A to B. Find the domain and range of the function f.

If B = [{:(-1, 0), (2, 4):}] " and " f(x) = x^(2) - 4x + 5, then find f(B).

If f:A toA where A={1,2,3,4,5,6,7,8,9,10} and f(x)={(x,,x is even),(x+1,,x is odd):} and g:A to A such that g(f(x))=f(x) . Find the number(s) of such function

int_0^9 f(x) dx, where f(x)={(sinx, if 0<=x < pi/2), (1, if pi/2 <= x < 3), (e^(x-3), if 3<=x<9):}

Which of the following relations are functions from A to B write their domain and range if it is not a function give reason ? f:A rarr B is defined by f={(1,-2),(3,7),(5,6),(9,0)},A={1,3,5,9},B={-2,7,-6,0,1,2}

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) .

If f(x)=a-(1)/(x+b), where a+b=1, then: (f@f@f)(x)=

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. State with reason whether following functions have inverse (i) f:{1,2...

    Text Solution

    |

  2. Find f^(-1) if it exists: f: A->B where A={0,\ -1,\ -3,\ 2}; B= {-9,\ ...

    Text Solution

    |

  3. Find f^(-1) if it exists: f: A->B where A={1,\ 3,\ 5,\ 7,\ 9}; B= {0,\...

    Text Solution

    |

  4. Show that the function f: Q->Q defined by f(x)=3x+5 is invertible. Als...

    Text Solution

    |

  5. Consider f: R->Rgiven by f(x) = 4x + 3. Show that f is invertible. Fin...

    Text Solution

    |

  6. Consider f\ : R+vec[4,oo) given by f(x)=x^2+4 . Show that f is inve...

    Text Solution

    |

  7. If f(x)=(4x+3)/(6x-4),\ x\ !=2/3, show that fof(x)=x for all x!=2/3dot...

    Text Solution

    |

  8. Consider f: R+->[-5,oo)given by f(x)=9x^2+6x-5. Show that f is inverti...

    Text Solution

    |

  9. If f: R->R be defined by f(x)=x^3-3 , then prove that f^(-1) exists an...

    Text Solution

    |

  10. A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not...

    Text Solution

    |

  11. If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=...

    Text Solution

    |

  12. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

    Text Solution

    |

  13. Consider f:R+->[-9,oo[ given by f(x)=5x^2+6x-9. Prove that f is invert...

    Text Solution

    |

  14. Let f: Nvec be a function defined as f(x)=9x^2+6x-5. Show that f: Nvec...

    Text Solution

    |

  15. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |