Home
Class 12
MATHS
Show that the modulus function f: RR rar...

Show that the modulus function `f: RR rarr RR` , given by ` f(x)=|x|` is neither one-one nor onto Where
`|x|={(x " when "x ge 0),(-x " when " x lt 0):}`

Promotional Banner

Topper's Solved these Questions

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2 B|6 Videos

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2 B (Very short answer type questions )|10 Videos

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|12 Videos

  • LOGARITHM

    CHHAYA PUBLICATION|Exercise Long Answer Type Question|12 Videos

  • MATHEMATICAL REASONING

    CHHAYA PUBLICATION|Exercise JEE Main (AIEEE) Archive (2016 )|1 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

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

Given, f (x) = x when x ge 0 = - x , when x lt 0

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

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

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

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.

Prove that the mapping f: RR rarr RR defined by , f(x)=x^(2)+1 for all x in RR is neither one-one nor onto.

Show that , the function f: RR rarr RR defined by f(x) =x^(3)+x is bijective, here RR is the set of real numbers.

Show that the signum function f:RR rarr RR , given by f(x)={(1" if "x gt 0),(0 " if "x = 0),(-1 " if " x lt0):} is neither one-one nor onto.

CHHAYA PUBLICATION-MAPPING OR FUNCTION-EXERCISE 2A ( very short answer type questions)
  1. Let A={0,1}, B={2,6} and f: A rarr B be given by, f(x)=6-4x and g: A r...

    Text Solution

    |

  2. Prove that the mapping f: RR rarr RR defined by ,f(x)=x^(2)+1 for all ...

    Text Solution

    |

  3. Prove that the mapping f: RR rarr RR defined by ,f(x)=x^(2)+1 for all ...

    Text Solution

    |

  4. Let A={-1,1,2,-3}, B={2,8,18,32} and f: A rarr B be defined by, f(x)=...

    Text Solution

    |

  5. Prove that the function f: RR rarr RR defined by, f(x)=sin x, for all...

    Text Solution

    |

  6. Show that the modulus function f: RR rarr RR , given by f(x)=|x| is n...

    Text Solution

    |

  7. Show that, the mapping f:NN rarr NN defined by f(x)=3x is one-one but ...

    Text Solution

    |

  8. Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bij...

    Text Solution

    |

  9. Let A be a finite set If f: A rarr A is an onto mapping , show that it...

    Text Solution

    |

  10. Let A be the set of quadrilaterals in a plane and RR^(+) be the set of...

    Text Solution

    |

  11. Let A={-1,1,-2,2},B={3,4,5,6} and f: A rarr B be the mapping defined b...

    Text Solution

    |

  12. Let D be the set of odd natural numbers . Then show that the mapping f...

    Text Solution

    |

  13. Show that, the mapping f: RR rarr RR defined by f(x)=mx +n, where m,n...

    Text Solution

    |

  14. Let A=RR-{2} and B=RR-{1}. Show that, the function f:A rarr B defined ...

    Text Solution

    |

  15. Let CC be the set of complex numbers and f:CC rarr RR be defined by f(...

    Text Solution

    |

  16. Show that the signum function f:RR rarr RR , given by f(x)={(1" if "...

    Text Solution

    |

  17. Let A={x in RR :-1 le xle 1} =B. Show that, the mapping f:A rarr B de...

    Text Solution

    |

  18. Let A={x in RR:-1 le x le 1} =B. Prove that , the mapping from A to B ...

    Text Solution

    |

  19. Prove that , the mapping f:NN rarr NN defined by, f(x)={(x+1 " when...

    Text Solution

    |

  20. Prove that the greatest integer function f: RR rarr RR, given by f(x)=...

    Text Solution

    |