Home
Class 12
MATHS
Show that a one-one function f : {1, 2, ...

Show that a one-one function `f : {1, 2, 3}-> {1, 2, 3}`must be onto.

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

If A={1,\ 2,\ 3} , show that an onto function f: A->A must be one-one

Let f : {1, 2, 3}->{a , b , c} be one-one and onto function given by f (1) = a , f (2) = b and f (3) = c . Show that there exists a function g : {a , b , c}->{1, 2, 3} such that gof=I_x and fog=I_y

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f: N->N , given by f(x)=2x , is one-one but not onto.

Show that the function f: N->N , given by f(x)=2x , is one-one but not onto.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f(x)=3x+ 2 is one-one and onto

Show that the function f:NtoN defined by f(x)=2x-1 is one-one but not onto.

Show that the function f: R-> R : f(x)=sinx is neither one-one nor onto

Prove that the function f : R ->R , given by f (x) = 2x , is one-one and onto.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Show that the exponential function f: R->R , given by f(x)=e^x , is...

    Text Solution

    |

  2. Show that the logarithmic function f: R0+->R given by f(x)=(log)a x...

    Text Solution

    |

  3. Show that a one-one function f : {1, 2, 3}-> {1, 2, 3}must be onto.

    Text Solution

    |

  4. If A={1,\ 2,\ 3} , show that an onto function f: A->A must be one-o...

    Text Solution

    |

  5. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  6. Give examples of two one-one functions f1 and f2 from R to R such t...

    Text Solution

    |

  7. Give examples of two surjective function f1 and f2 from Z to Z such...

    Text Solution

    |

  8. Show that if f1 and f2 are one-one maps from R to R , then the product...

    Text Solution

    |

  9. Suppose f1 and f2 are non-zero one-one functions from R to R . Is (...

    Text Solution

    |

  10. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

    Text Solution

    |

  11. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

    Text Solution

    |

  12. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

    Text Solution

    |

  13. Show that f: R->R , given by f(x)=x-[x] , is neither one-one nor onto.

    Text Solution

    |

  14. Let f: N->N be defined by: f(n)={(n+1)/2, if n is odd (n-1)/2, if n i...

    Text Solution

    |

  15. Let R be the set of real numbers. If f: R->R :f(x)=x^2 and g: R->R ...

    Text Solution

    |

  16. Let : R->R ; f(x)=sinx and g: R->R ; g(x)=x^2 find fog and gof .

    Text Solution

    |

  17. Let f:{2,3,4,5}vec{3,4,5,9}a n dg:{3,4,5,9}vec{7, 11 , 15} be function...

    Text Solution

    |

  18. Let f:{1,\ 3,4\ }->{1,\ 2,\ 5} and g:{1,\ 2,\ 5}->{1,\ 3} be given by ...

    Text Solution

    |

  19. Find gof and fog , if f: R->R and g: R->R are given by f(x)=|x| and g(...

    Text Solution

    |

  20. If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} ...

    Text Solution

    |