Home
Class 12
MATHS
Show that the function f:N rarr N , give...

Show that the function `f:N rarr N` , given by f(1) = f(2) = 1 and f(x) = x - 1, for every `x gt 2` , is onto but not one-one.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|19 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|30 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|64 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

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

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

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

Show that the Signum Function f : R rarr R given by f(x) = {(1," if " x gt0),(0," if " x =0),(-1," if " x lt0):} is neither one - one nor onto.

The domain of the function f given by f(x)= (x^(2) + 2x + 1)/(x^(2)-x-6)

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 number . is the result true, if the domain R is replaced by N with co-domain being same as R ?

Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1 , "if x is even"):} is both one - one and onto .

Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) =x/(1+|x|),x in R is one one and onto function.

Let the function f : R rarr R be defined by f(x) = cos x , AA x in R . Show that f is nether one - one nor onto .

Find the range of the following function f: N rarr R, f(x)= (1)/(x)

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Show that the function f:N rarr N , given by f(x) = 2x, is one-one but...

    Text Solution

    |

  2. Prove that the function f :R rarr R , given by f(x) = 2x, is one-one a...

    Text Solution

    |

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

    Text Solution

    |

  4. Show that the function f: R rarr R , defined as f(x) = x^2 , is neithe...

    Text Solution

    |

  5. Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Let f: {2, 3, 4, 5} rarr {3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 1...

    Text Solution

    |

  9. Find gof and fog, if f:R rarr R and g: R rarrR are given by f(x) = c...

    Text Solution

    |

  10. Show that if f: R - {7/5} rarr R - {3/5} is defined by f(x) = (3x+4)/...

    Text Solution

    |

  11. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

    Text Solution

    |

  12. Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr ...

    Text Solution

    |

  13. Consider functions f and g such that composite gof is defined and is o...

    Text Solution

    |

  14. Are fand g both necessarily onto, if gof is onto?

    Text Solution

    |

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

    Text Solution

    |

  16. Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y...

    Text Solution

    |

  17. Let Y = {n^(2) :n in N} subN Consider f: N rarr Y as f(n) = n^2 . Sh...

    Text Solution

    |

  18. Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . ...

    Text Solution

    |

  19. Consider f: N rarr N,g :N rarr N and h: Nrarr R defined as f(x) = 2x, ...

    Text Solution

    |

  20. Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} de...

    Text Solution

    |