Home
Class 12
MATHS
Let f : {1, 2, 3}->{a , b , c}be one-one...

Let `f : {1, 2, 3}->{a , b , c}`be one-one and onto function given by `f (1) = a`, `f (2) = b`and `f (3) = c`. Show that there exists a function `g : {a , b , c}->{1, 2, 3}`such that `gof=I_x`and `fog=

Text Solution

Verified by Experts

The correct Answer is:
`I _(y)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.1|16 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

Let f: {1, 2, 3} rarr {a,b,c} be one-one and onto function given by f(1) = a, f(2) = b and f(3) = C. Show that there exists a function g: {a,b,c} rarr {1,2,3} such that gof =I_(x) and fog = I_Y , where X = {1,2,3} and Y = {a,b,c} ,

Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be onto.

Consider f : {1,2,3} rarr {a,b,c} given by f(1) = a, f(2) and f(3) = c . Find f^(-1) and show that (f^(-1))^(-1)=f .

Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one-one.

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

Show that the function f:N rarr N , given by f(1) = f(2) = 1 and f(x) = x - 1, for every x gt 2 , is onto but not one-one.

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

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Let f : {1, 2, 3}->{a , b , c}be one-one and onto function given by f...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  4. If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)}.

    Text Solution

    |

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

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  9. Given a non-empty set X , consider P\ (X) which is the set of all subj...

    Text Solution

    |

  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  13. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

    Text Solution

    |

  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  15. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |