Home
Class 12
MATHS
Show that an onto function f : {1, 2, 3}...

Show that an onto function `f : {1, 2, 3} rarr {1, 2, 3}` is always one-one.

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

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

Let f : { 1, 2, 3} rarr {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} rarr { 1, 2, 3} such that gof = I_x and fog = l_y . where X = {1, 2, 3} and Y = {a, b, c} .

Show that the function f: N rarrN given by f(x)= 3x is one-one but not onto.

Show that the function f(x) = 2x+9 is one-one.

Show that function defined by f: N rarr N , f (x) = x^3 is one-one but not onto.

Show that the function f : R_* rarr R_* defined by f (x) = 1/x is one-one and onto, where R_* is the set of all non-zero real numbers. Is the result true, if the domain R_* is replaced by N with co-domain being same as R_* ?

Show that function defined by f: Zrarr Z , f (x) = x^3 is one-one but not onto.

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

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

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

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one-...

    Text Solution

    |

  2. Which one of the following graph represents the function of x? Why?

    Text Solution

    |

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

    Text Solution

    |

  4. Let A be the set of all 50 students of class XII in a school. Let f: A...

    Text Solution

    |

  5. Prove that the function f : RrarrR given by f (x) = 2x is one-one and...

    Text Solution

    |

  6. Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x...

    Text Solution

    |

  7. Show that function f: Rrarr R given by f(x) = x^2 is neither one-one n...

    Text Solution

    |

  8. Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,i...

    Text Solution

    |

  9. If f : R rarr R is defined by f(x) = x + 2, find f(f(x))

    Text Solution

    |

  10. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

    Text Solution

    |

  11. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

    Text Solution

    |

  12. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find gof.

    Text Solution

    |

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

    Text Solution

    |

  14. Let f(x) = (4x+3)/(6x-4), x ne 2/3 .show that fof (x) = x.

    Text Solution

    |

  15. Find gof and fog if f: RrarrR and g: R rarr R are given by f(x) = co...

    Text Solution

    |

  16. If the function f : R rarr R given by f(x) = x^2 +2 and g RrarrR be g...

    Text Solution

    |

  17. Let f : { 1, 2, 3} rarr {a, b, c} be one-one and onto function given b...

    Text Solution

    |

  18. Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by ...

    Text Solution

    |

  19. Let Y = {n^2 : n in N} sub N Consider f : N rarr Y as f (n) = n^2 Show...

    Text Solution

    |

  20. Let f: Nrar R be a function defined as : f(x) = 4x^2 + 12 x + 15. Sho...

    Text Solution

    |

  21. Let f : N rarr N be a function deifned by f(x) = 9x^2 + 6x - 5. Show ...

    Text Solution

    |