Home
Class 12
MATHS
Let f: N-{1}->N be defined by, f(n)= the...

Let `f: N-{1}->N` be defined by, `f(n)=` the highest prime factor of `n` . Show that `f` is neither one-one nor onto. Find the range of `fdot`

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

Let f: N-[1]vecN be defined by, f(n)= the highest prime factor of n . Show that f is neither one-one nor onto. Find the range of fdot

Let f: N-[1]vecN be defined by, f(n)= the highest prime factor of n . Show that f is neither one-one nor onto. Find the range of fdot

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let A = {9, 10 , 11 , 12 , 13} and let f : A ->N be defined by f(n) = the highest prime factor of n. Find the range of f.

Let A = {9, 10 , 11 , 12 , 13} and let f : A ->N be defined by f(n) = the highest prime factor of n. Find the range of f.

Let A = {9, 10 , 11 , 12 , 13} and let f : A ->N be defined by f(n) = the highest prime factor of n. Find the range of f.

Let the function f:R→R be defined by f(x)=cosx,∀x∈R. Show that f is neither one-one nor onto

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

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=...

    Text Solution

    |

  2. Let A be any non-empty set. Then, prove that the identity function on ...

    Text Solution

    |

  3. Let f: N-{1}->N be defined by, f(n)= the highest prime factor of n ...

    Text Solution

    |

  4. Let A={1,2} . Find all one-to-one function from A to A.

    Text Solution

    |

  5. Consider the identity function IN : N->N defined as, IN(x)=x for al...

    Text Solution

    |

  6. Consider a function f:[0,pi/2]->R given by f(x)=sin x and g:[0,pi/2]->...

    Text Solution

    |

  7. Let f:X->Y be a function. Define a relation R in X given by R={(a,b):f...

    Text Solution

    |

  8. Show that the function f: R->{x in R :-1ltxlt1} defined by f(x)=x/(1+...

    Text Solution

    |

  9. Show that the function f: R->R given by f(x)=x^3+x is a bijection.

    Text Solution

    |

  10. check that f : N- N defined by f(n)={(n+1)/2,(if n is odd)),(n/2,(if ...

    Text Solution

    |

  11. Show that the function f: N->N given by, f(n)=n-(-1)^n for all n in N...

    Text Solution

    |

  12. Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ e v e nn-1...

    Text Solution

    |

  13. Let A be a finite set. If f: A->A is a one-one function, show that ...

    Text Solution

    |

  14. Let A be a finite set. If f: A->A is an onto function, show that f ...

    Text Solution

    |

  15. Give an example of a function which is one-one but not onto. whi...

    Text Solution

    |

  16. Which of the following functions from A to B are one-one and onto? ...

    Text Solution

    |

  17. Prove that the function f: N->N , defined by f(x)=x^2+x+1 is one-on...

    Text Solution

    |

  18. Let A={-1,\ 0,\ 1} and f={(x ,\ x^2): x in A} . Show that f: A->A is ...

    Text Solution

    |

  19. Classify f: N->N given by f(x)=x^2 as injection, surjection or bije...

    Text Solution

    |

  20. Classify f: Z->Z given by f(x)=x^2 as injection, surjection or bije...

    Text Solution

    |