Home
Class 12
MATHS
If f: Z->Z be defined by f(x)=2x for all...

If `f: Z->Z` be defined by `f(x)=2x` for all `x in Z` . Find `g: Z->Z` such that `gof=I_Z` .

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

Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=I_Z .

Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=I_Z .

Show that the function f: ZvecZ defined by f(x)=x^2+x for all x in Z , is a many one function.

Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , is a function but not bijective function.

If f: Z to Z be given by f(x)=x^(2)+ax+b , Then,

Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in Z .

Classify f: Z->Z , defined by f(x)=x^2+x as injection, surjection or bijection.

Classify f: Z->Z , defined by f(x)=x-5 as injection, surjection or bijection.

Find the inverse of the function: f:Z to Z defined by f(x)=[x+1], where [.] denotes the greatest integer function.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f,g: R -R are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fi...

    Text Solution

    |

  2. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

    Text Solution

    |

  3. If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such t...

    Text Solution

    |

  4. Let f,\ g and h be functions from R to R . Show that (f+g)oh=foh+goh

    Text Solution

    |

  5. Let f,\ g and h be functions from R to R . Show that (fog)oh=(foh)(goh...

    Text Solution

    |

  6. Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0...

    Text Solution

    |

  7. Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx i...

    Text Solution

    |

  8. Let f: RvecR and g: Rvec be two functions such that fog(x)=sinx^2a n...

    Text Solution

    |

  9. If f: R->R be given by f(x)=sin^2x+sin^2(x+pi//3)+cosx\ cos(x+pi//3) f...

    Text Solution

    |

  10. Let f: ZvecZ be defined by f(n)=3n for all n in Z and g: Zvec be defi...

    Text Solution

    |

  11. Let f: R->R be a function given by f(x)=a x+b for all x in R . Find t...

    Text Solution

    |

  12. Let f: A->A be a function such that fof=f . Show that f is onto if and...

    Text Solution

    |

  13. Let f,g: R-R be two functions defined as f(x)=|x|+x and g(x)=|x|-x , f...

    Text Solution

    |

  14. Find gof and fog when f: R->R and g: R->R is defined by f(x)=2x+3 and ...

    Text Solution

    |

  15. Find gof and fog when f: R->R and g: R->R is defined by f(x)=2x+x^2 an...

    Text Solution

    |

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

    Text Solution

    |

  17. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x and g(x...

    Text Solution

    |

  18. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x^2+2x-3 ...

    Text Solution

    |

  19. Find gof and fog when f: R->R and g: R->R is defined by f(x)=8x^3 and ...

    Text Solution

    |

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

    Text Solution

    |