Home
Class 12
MATHS
A function f from the set of natural ...

A function `f` from the set of natural numbers to integers defined by `f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d-n/2,\ w h e n\ n\ i s\ e v e n` is (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

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

A function f from the set of natural numbers to integers is defined by n when n is odd f(n) =3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and onto (b) one-one but not onto (c) onto but not one-one (d) neither one-one nor onto

If f:[0,oo)->[0,oo) and f(x)=x/(1+x), then f(x) is (a) one-one and onto (b)one-one but not onto (c)onto but not one-one (d)neither on-one nor onto

Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s\ od d . Then, f is (a) onto but not one-one (b) one-one but not onto (c) one-one and onto (d) neither one-one nor onto

Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) onto but not one-one (d) neither one-one nor onto

The function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then is (a) one-one and onto (b) one-one and into (c) many-one and onto (d) many-one and into

If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is - (a)f is one-one and onto (b)f is one-one but onto (c)f is onto but not one-one (d)the range of f is equal to its domain

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

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

    Text Solution

    |

  2. The function f: R->R , f(x)=x^2 is (a) injective but not surjective (b...

    Text Solution

    |

  3. A function f from the set of natural numbers to integers defined by...

    Text Solution

    |

  4. Which of the following functions from A={x in R :-1lt=xlt=1} to its...

    Text Solution

    |

  5. Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s...

    Text Solution

    |

  6. The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and on...

    Text Solution

    |

  7. Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation fo...

    Text Solution

    |

  8. If f(x)=3x-5, then f^(-1)(x) (a) is given by 1/((3x-5)) (b) is given...

    Text Solution

    |

  9. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then (a).f(x)=sin^2x ,g...

    Text Solution

    |

  10. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  11. If the function f:(1,oo) vec (1,oo) is defined by f(x)=2^(x(x-1)),t h ...

    Text Solution

    |

  12. Let A={x in R : xlt=1} and f: A->A be defined as f(x)=x(2-x). Then, f...

    Text Solution

    |

  13. Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=(a) x for all x in R...

    Text Solution

    |

  14. If the function f: R->R be such that f(x) = x-[x], where [x] denotes t...

    Text Solution

    |

  15. If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals....

    Text Solution

    |

  16. Let g(x)=1+x-[x]a n df(x)={-1, x<0;0, if x=0;1, ifx >0 . Then for all ...

    Text Solution

    |

  17. Let f(x)=(alphax)/((x+1)),x!=-1. for what value of alpha is f(f(x))=x ...

    Text Solution

    |

  18. The distinct linear functions which map [-1, 1] onto [0, 2] are f(x...

    Text Solution

    |

  19. If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

    Text Solution

    |

  20. If f: Rvec(-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) e...

    Text Solution

    |