GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
111 views

Consider a function f:A->B is bijective ..which of the following is INCORRECT?

a)f-1 :B->A exist

b)f-1 : B->A unique

c)f-1 is bijective

d) None of these

asked in Set Theory & Algebra by Veteran (18.2k points)   | 111 views
Answer is D.

for inverse to hold a function should be bijective.

So here (a) is correct....

likewise (b) and (c) are also properties of an inverse functions...you can look up any standard textbook..
Change your comment to answer @Aditya Tewari

1 Answer

+4 votes
Best answer

If function is bijective then it is one to one and onto . 

Function is invertable it is bijective. so inverse is possible.

Function is one to one and onto means bumber of element is same in A and B  since one to one inverse also one to one so unique.

Inverse of bijective funtion is bijective always.

 

answered by Veteran (44.8k points)  
selected by


Top Users Mar 2017
  1. rude

    4768 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2734 Points

  5. Debashish Deka

    2592 Points

  6. 2018

    1544 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1342 Points

  9. Bikram

    1312 Points

  10. Sanjay Sharma

    1126 Points

Monthly Topper: Rs. 500 gift card

21,508 questions
26,832 answers
61,091 comments
23,146 users