Home
Class 12
MATHS
If function f:AtoB is a bijective , then...

If function `f:AtoB` is a bijective , then `f^(-1)` of is

A

`fof^(-1)`

B

`f`

C

`f^(-1)`

D

`I_(A)` (the identity map of the set A)

Text Solution

Verified by Experts

The correct Answer is:
D
`f : A rarr B`
f is a function, then `f^(-1)` is also a bijective function. Composite function `(f^(-1) of) = I_(A)`
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|3 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|6 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 3|10 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

Similar Questions

Explore conceptually related problems

Let f:ArarrB is a function defined by f(x)=(2x)/(1+x^(2)) . If the function f(x) is a bijective function, than the correct statement can be

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

If f:AtoB and g:BtoC are both bijective functions then (gof)^(-1) is

Let f : A to B and g : B to C be the bijective functions. Then (g of )^(-1) is

Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)) then --(1) f is bijection (2) f is an injection only (3) f is a surjection (4) f is neither injection nor a surjection

If A=R-{b} and B=R-{1} and function f:AtoB is defined by f(x)=(x-a)/(x-b),aneb then f is

A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not? In case it is a bijection, find f^(-1)(3) .

If A=R-{b} and B=R-{1} and function f:AtoB is defined by f(x)=(x-a)/(x-b),aneb , then f^(-1)(x) is

Let f : N->N be defined by f(n)={(n+1)/2,"if n is odd " n/2,"if n is even " for all n in N . State whether the function f is bijective. Justify your answer.

ARIHANT MATHS ENGLISH-SETS, RELATIONS AND FUNCTIONS -Exercise (Single Option Correct Type Questions)
  1. For n,mepsilonN,n|m means that n is a factor of m then relation | is

    Text Solution

    |

  2. Find all congruent solutions of 8x -= 6 (mod 14).

    Text Solution

    |

  3. Let A be a set containing 10 distinct elements. Then the total number ...

    Text Solution

    |

  4. Let A and B be two non- empty subsets of a set X such that A is not a ...

    Text Solution

    |

  5. f and h are function from A rarr B, where A = {a, b, c, d} and B = {s,...

    Text Solution

    |

  6. Let I be the set of integer and f : I rarr I be defined as f(x) = x^(2...

    Text Solution

    |

  7. Which of the four statements given below is different from other?

    Text Solution

    |

  8. Let A={1,\ 2,\ ,\ n} and B={a ,\ b} . Then the number of subjectio...

    Text Solution

    |

  9. If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

    Text Solution

    |

  10. f:R to R is a function defined by f(x)=10x -7, if g=f^(-1) then g(x)=

    Text Solution

    |

  11. Let R be a relation defined by R = {(a, b) : a ge b}, where a and b a...

    Text Solution

    |

  12. If the sets A and B are defined are defined as A={(x,y):y=e^x, x in R}...

    Text Solution

    |

  13. If function f:AtoB is a bijective , then f^(-1) of is

    Text Solution

    |

  14. If f(y) = (y)/(sqrt(1-y^(2))), g(y) = (y)/(sqrt(1+y^(2))), then (fog) ...

    Text Solution

    |

  15. f:R->R is defined as f(x)=2x+|x| then f(3x)-f(-x)-4x=

    Text Solution

    |

  16. Let R and S be two non-void relations on a set A. Which of the followi...

    Text Solution

    |

  17. Let f:R to R, g: R to R be two functions given by f(x)=2x-3,g(x)=x^(3)...

    Text Solution

    |

  18. If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to ...

    Text Solution

    |

  19. If f: RvecRvecR are two given functions, then prove that 2m indot{if(x...

    Text Solution

    |

  20. Let f: RvecRa n dg: RvecR be two given functions such that f is inject...

    Text Solution

    |