Home
Class 12
MATHS
Let A =R-{3} and B=R-{1}. Consider the f...

Let `A =R-{3}` and `B=R-{1}`. Consider the function `f : A to B` defined by `f(x) = ((x-2)/(x-3))`. Is f one-one and onto? Justify your answer.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTION

    MODERN PUBLICATION|Exercise EXAMPLE|212 Videos
  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|543 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos

Similar Questions

Explore conceptually related problems

Let A= R-{3}" and "B= R-{1} . Consider the function f : A to B defined by f(x)= (x-2)/(x-3) . Then f is………..

Let A=R-{3} and B=R-{1} . Consider the function f:A–>B . defined by f(x)= (x-2)/(x-3) Is f one one or Onto? Justify your answer

Show that the function f: R rarr R defined by f(x) = (3x-1)/2, x in R is one-one and onto function.

Show. that the function f: R rarr R defined by f(x)= (3x-1)/3, x inR is one-one and onto function.

Show that the function f: R rarr R defined by f(x) = (4x-3)/5, x in R is one one and onto function.

Let a function f:R rarr R be defined by f(x) = 3 - 4x Prove that f is one-one and onto.

A function f: R rarr R be defined by f(x) = 5x+6. prove that f is one-one and onto.

Let f : R rarr R be defined by f(x) = cos (5x+2). Is f invertible? Justify your answer.

Prove that the function f: R rarr R defined by f(x) = 2x + 5 is one-one.

Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by f(x)= (x-2)/(x-3) show that f is one -one and onto, hence find f^(-1) .

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Let A and B be sets, show that f : A xx B rarr B xx A such that f(a,b...

    Text Solution

    |

  2. Let f: N to N be defined by f(n) = {{:((n+1)/2, " if n is odd "),(n/2,...

    Text Solution

    |

  3. Let A =R-{3} and B=R-{1}. Consider the function f : A to B defined by ...

    Text Solution

    |

  4. Let f : R rarr R be defined as f(x) = x^4. Choose the correct answer.

    Text Solution

    |

  5. Let f : RrarrR be defined as f (x) = 3x Choose the correct answer.

    Text Solution

    |

  6. If f:(1,3,4} rarr {1, 2,5} and g:(1,2,5) {1,3} be given by f = {(1, 2)...

    Text Solution

    |

  7. Let f,g and h be function from R to R. Show that (f+g) o h = foh + goh

    Text Solution

    |

  8. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

    Text Solution

    |

  9. Find gof and fog, if f(x) = 8x^3 and g(x) = x^(1/3)

    Text Solution

    |

  10. If f(x)=(4x+3)/(6x-4) , x ne 2/3 , show that (fof) (x) = x for all ne ...

    Text Solution

    |

  11. State with reason whether following functions have inverse: h: {2,3,4,...

    Text Solution

    |

  12. State with reason whether following functions have inverse: g: {5,6,7,...

    Text Solution

    |

  13. State with reason whether following functions have inverse: h: {2,3,4,...

    Text Solution

    |

  14. Show that f: [ -1, 1] rarr R, given by f(x)= (x)/(x+2) is one-one. Fin...

    Text Solution

    |

  15. Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. ...

    Text Solution

    |

  16. Consider f : R+rarr [4, oo) given byf (x) = x^2 + 4 Show that f is inv...

    Text Solution

    |

  17. Consider f: Rrarr[-5, oo] given by f(x) = 9x^2 + 6x - 5. Show that f ...

    Text Solution

    |

  18. Let f : X rarr Y be an invertible function. Show that f has unique inv...

    Text Solution

    |

  19. Consider f : {1, 2, 3} rarr {a, b, c}, given by f (1) = a, f (2) = b ...

    Text Solution

    |

  20. Let f : X rarr Y be an invertible function. Show that the inverse of ...

    Text Solution

    |