Home
Class 12
MATHS
Consider f : {1, 2, 3} rarr {a, b, c} gi...

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

Text Solution

Verified by Experts

f^(-1){a, b, c}={1,2,3}.
.f^(-1){1,2 , 3}={a, b, c} ,.
i.e. .(f^-1)^(-1)=f.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

  • THREE DIMENSIONAL GEOMETRY

    V PUBLICATION|Exercise QUESTION BANK|103 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 . Shów that there exists a function g:{a, b, c} rarr {1,2,3.} such that g o f=I_x and f o g=, I_ y where, X={1,2,3} and Y={a, b, c}

If f (x) =1/(1 - x) , show that f(f(f(x))) = x

Let f:RtoR be given by f(x)=frac(2x+1)(3) find fof and show that f is invertible.

If f : R rarr R be given by f(x) = (3 - x^3)^(1/3) , then (f o f) (x) is

If f(x)=x+1/x show that (f(x))^3=f(x^3)+3 f(x)

If (1, xle 3) , (ax+b , 3 find f(3^+) and f(3^-)

Let f,g: R rarr R be defined, respectively by f (x) = x + 1,g (x) = 2x -3 . find f + g,f - g and f/g

Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.

Consider the set A={1,2,3,4,5} , and B={1,4,9,16,25} and a function f:AtoB defined by f(1)=1 , f(2)=4 , f(3)=9 , f(4)=16 and f(5)=25 . Show that f is one-to-one.

Consider the set A={1,2,3,4,5} , and B={1,4,9,16,25} and a function f:AtoB defined by f(1)=1 , f(2)=4 , f(3)=9 , f(4)=16 and f(5)=25 . Show that f is onto.

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Consider f:R^+to[-5, infty) given by f(x)=9x^2+6x-5. Show that f is ...

    Text Solution

    |

  2. Let f : X rarr Y be invertible, show that f has unique inverse

    Text Solution

    |

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

    Text Solution

    |

  4. Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, ...

    Text Solution

    |

  5. If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) i...

    Text Solution

    |

  6. f : R - {(-4)/3} rarr R be a function defined as f(x) = (4x)/(3x +4). ...

    Text Solution

    |

  7. Can you define a function from 'RxR rarr R' such as 'f3: RxR rarr, R' ...

    Text Solution

    |

  8. Can yóu define a function from 'R xx R rarr R' such as 'f4: R xx R rar...

    Text Solution

    |

  9. Show that addition, subtraction and multiplication are binary opera...

    Text Solution

    |

  10. Show that subtraction and division are not binary operations on N.

    Text Solution

    |

  11. Show that *: R xx R rarr R is given by (a, b) rarr(a+4 b)^2 is a binar...

    Text Solution

    |

  12. Let P be the set of all subsets of a given set X. Show that uu: P xx P...

    Text Solution

    |

  13. Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and t...

    Text Solution

    |

  14. Show that +: R xx R rarr R and xx: R xx R rarr R are commutative binar...

    Text Solution

    |

  15. Show that *: R xx R rarr R defined by a * b=a+2 b is not commutative.

    Text Solution

    |

  16. Show that addition and multiplication are associativé binary operation...

    Text Solution

    |

  17. Show that * :R xx R rarr R given by a* b= a+2 b is not associative.

    Text Solution

    |

  18. Show that zero is the identity for addition on R and 1 is the identity...

    Text Solution

    |

  19. Show that - a is not the inverse of a in N for the addition operation ...

    Text Solution

    |

  20. Determine whether or not each of the definitions of ** given below giv...

    Text Solution

    |