Home
Class 12
MATHS
Let f: Z->Z be defined by f(x)=x+2. Find...

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

Text Solution

Verified by Experts

Let `{x} in {Z}`.

Then,

` (g circ f)=I_{z} Rightarrow(g circ f)(x)=I_{z}(x) `

`Rightarrow g[f(x)]=x `

`Rightarrow g(2 x)=x`

`Rightarrow g(y)=frac{1}{2} y[text { where } 2 x=y]`

...
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

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

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

Let f:N rarr Z be a function defined as f(x)=x-1000. Show that f is an into function.

C is the complex numvers f:CrarrR is defined by f(z)=|z^(3)-z+2|. Find the maximum value of f(z),If|z|=1.

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

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

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

Which of the following functions has inverse function? f:Z rarr Z defined by f(x)=x+2f:Z rarr Z defined by f(x)=2xf:Z rarr Z defined byy f(x)=xf:Z rarr Z defined by f(x)=|x|

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

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

    Text Solution

    |

  2. If f: ArightarrowA ,g: ArightarrowA are two bijections, then prove tha...

    Text Solution

    |

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

    Text Solution

    |

  4. Which one the following relations on A={1,2,3} is function? f={(1,3),(...

    Text Solution

    |

  5. Write the domain of the real function f defined by f(x)=sqrt(25-x^2) .

    Text Solution

    |

  6. Let A}x :-1lt=xlt=1}a n df: Avec such that f(x)=x|x|, then f is a bije...

    Text Solution

    |

  7. If the function f:(1,oo)rarr(1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |

  8. If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x...

    Text Solution

    |

  9. Let f be a real function defined by f(x)=sqrt(x-1.) Find (fofof)(x)dot...

    Text Solution

    |

  10. Let f: R-> R be the function defined by f(x)=4x−3 for all x in R. Then...

    Text Solution

    |

  11. Find whether f: R->R given by f(x)=x^3+2 for all x in R .

    Text Solution

    |

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

    Text Solution

    |

  13. Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , i...

    Text Solution

    |

  14. Discuss the surjectivity of f: R->R given by f(x)=x^3+2 for all x i...

    Text Solution

    |

  15. Discuss the surjectivity of f: R->R given by f(x)=x^2+2 for all x i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |