Home
Class 12
MATHS
Show that f: RvecR , given by f(x)=x-[x]...

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

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

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

Show that the modulus function f: R->R , given by f(x)=|x| is neither one-one nor onto.

Show that the function f: RvecR given by f(x)=cosxfora l lx in R , is neither one-one nor onto

Prove that the Greatest Integer Function f : R->R , given by f (x) = [x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Prove that the greatest integer function f: RR rarr RR , given by f(x)=[x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Let C and R denote the set of all complex numbers and all real numbers respectively. Then show that f: C->R given by f(z)=|z| for all z in C is neither one-one nor onto.

Show that the function f: R->R given by f(x)=cosx for all x in R , is neither one-one nor onto.

Show that the Modulus Function f : R->R , given by f (x) = | x | , is neither one-one nor onto, where | x | is x, if x is positive or 0 and | x | is x , if x is negative.

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

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

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f: R->R be the function defined by f(x)=4x^3+7, show that f is a ...

    Text Solution

    |

  2. Let A={1,2,3}dot Write all one-one from A to itself.

    Text Solution

    |

  3. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor on...

    Text Solution

    |

  4. Suppose f1a n df2 are non-zero one-one functions from RtoRdot is (f1...

    Text Solution

    |

  5. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and g ={(1,\ 3),\ (3,\ 3),\ (4,\...

    Text Solution

    |

  6. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

    Text Solution

    |

  7. Let f: RvecR and g: RvecR be defined by f(x)=x^2 and g(x)=x+1. Show ...

    Text Solution

    |

  8. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

    Text Solution

    |

  9. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

    Text Solution

    |

  10. Let f: RrarrR and g: RrarrR be defined by f(x)=x+1 and g(x)=x-1....

    Text Solution

    |

  11. Show that the exponential function f: R to R , given by f(x)=e^x , i...

    Text Solution

    |

  12. Let A="{"-1,0,1")"a n df={(x , x^2): xA}dot Show that f: AvecA is neit...

    Text Solution

    |

  13. If f: AvecB is an injection such that range of f={a}dot Determine t...

    Text Solution

    |

  14. Which of the following functions from AtoB are one-one and onto? ...

    Text Solution

    |

  15. Prove that the function F : NtoN , defined by f(x)=x^2+x+1 is one-on...

    Text Solution

    |

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

    Text Solution

    |

  17. Let A=R-[2] \ a n d \ B=R-[1]. If f: A->B is a mapping defined by f(x)...

    Text Solution

    |

  18. Show that if f1a n df1 are one-one maps from RtoR , then the pro...

    Text Solution

    |

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

    Text Solution

    |

  20. If f,g: R -R are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fi...

    Text Solution

    |