Home
Class 12
MATHS
Show that the Signum function f:R->R, gi...

Show that the Signum function `f:R->R`, given by `f(x)={(1,xgt0),(0,x=0),(-1,xlt0))` is neither one-one nor onto

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

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.

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 function f(x) given by f(x)={(xsin(1/x),x!=0),(0,x=0):} is continuous at x = 0

Show that the function f:R->R defined by f(x)=x/(x^2+1) AA x in R is neither one-one nor onto. Also if g:R->R is defined by g(x)=2x-1 find fog(x)

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.

Show that the logarithmic function f: R0+->R given by f(x)=(log)_a x ,\ a >0 is a bijection.

Show that the function f: RvecR given by f(x)=cosxfora l lx 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.

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 logarithmic function f: R0+vecR given by f(x)=(log)_a x ,a >0 is bijection.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in...

    Text Solution

    |

  2. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

    Text Solution

    |

  3. Show that the Signum function f:R->R, given by f(x)={(1,xgt0),(0,x=0),...

    Text Solution

    |

  4. Prove that the function f: Q->Q given by f(x)=2x-3 for all x in Q ...

    Text Solution

    |

  5. Show that the function f: R->R defined by f(x)=3x^3+5 for all x in R ...

    Text Solution

    |

  6. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

    Text Solution

    |

  7. Let A be the set of all 50 students of class X I I in a central scho...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Show that the function f : R ->R, defined as f(x)=x^2, is neither one-...

    Text Solution

    |

  11. Show that f: R->R , defined as f(x)=x^3 , is a bijection.

    Text Solution

    |

  12. Show that the function f: R0->R0 , defined as f(x)=1/x , is one-one on...

    Text Solution

    |

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

    Text Solution

    |

  14. Show that the modulus function f: R->R , given by f(x)=|x| is neith...

    Text Solution

    |

  15. Let C be the set of complex numbers. Prove that the mapping F:C to R g...

    Text Solution

    |

  16. Show that the function f: Rvec given by f(x)=x a+b , where a , b in R...

    Text Solution

    |

  17. Show that the function f: R->R given by f(x)=cosx for all x in R , is...

    Text Solution

    |

  18. Let A=R-{2} and B=R-{1} . If f: A->B is a mapping defined by f(x)=(...

    Text Solution

    |

  19. Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=...

    Text Solution

    |

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

    Text Solution

    |