Home
Class 12
MATHS
Prove that f: R->R , given by f(x)=2x , ...

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

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

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

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

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

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

Show that f: RvecR , 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 exponential function f: R->R , given by f(x)=e^x , is one-one but not onto. What happens if the co-domain is replaced by R0+ (set of all positive real numbers).

Write whether f: R->R given by f(x)=x+sqrt(x^2) is one-one, many-one, onto or into.

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

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A be the set of all 50 students of class X I I in a central scho...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |