|

Differential Calculus

Blazing goIITian

 Joined: 5 Jun 2007 Post: 978
16 Apr 2009 12:31:07 IST
0 People liked this
15
769
bijection or not??
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Differential Calculus

Let f:R->R be given by f(x) = (x+1)2 - 1 , x-1. Find inverse of x.

a) f -1(x) = -1 +

b) f -1(x) = -1 -

c) f -1(x) = -1

d) f -1(x) =

The answer given is (a) which is indeed the answer if f is a bijection.

But how is f bijection??

injectivity can be proved. But surjectivity of 'f' is not possible.

Putting y = f(x) we get

x = -1 + . and so for y-1, x doesn't exist. But y-1 is in the codomain.

So Range  Codomain.

Hence it is not surjecton. So f is not invertible.

Blazing goIITian

Joined: 6 Aug 2007
Posts: 1860
16 Apr 2009 13:37:56 IST
1 people liked this

since x is greater than 1...it is bijective....

Blazing goIITian

Joined: 7 Aug 2008
Posts: 1047
16 Apr 2009 13:39:23 IST
1 people liked this

it shud be bijective

Blazing goIITian

Joined: 11 Mar 2009
Posts: 5564
16 Apr 2009 13:40:50 IST
2 people liked this

totally agreed biki....it is not invertible in R--->R ..

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
16 Apr 2009 14:15:06 IST
1 people liked this

for x -1

all values of y dont satisfy...

Here the range of the function for x -1 is y -1. But the codomain is R.

So RangeCodomain.

So it is not onto function and hence cannot be inverted...

For function to be invertible, the codomain should have been [ -1, ).

Am i not correct???

Blazing goIITian

Joined: 11 Mar 2009
Posts: 5564
16 Apr 2009 14:17:01 IST
2 people liked this

yes ..function is only invertible if codomain is [-1,infinity)..totally agreed ..thats wat i m saying ..function not invertible

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
16 Apr 2009 14:34:24 IST
1 people liked this

for x -1

all values of y dont satisfy...

Here the range of the function for x -1 is y -1. But the codomain is R.

So RangeCodomain.

So it is not onto function and hence cannot be inverted...

For function to be invertible, the codomain should have been [ -1, ).

Am i not correct???

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
18 Apr 2009 23:27:56 IST
1 people liked this

please tell... is the question wrong or not... the graph shows it is..

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
19 Apr 2009 10:38:48 IST
1 people liked this

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
19 Apr 2009 22:28:54 IST
1 people liked this

Blazing goIITian

Joined: 1 Apr 2007
Posts: 1084
20 Apr 2009 13:27:26 IST
1 people liked this

friend...they themselves hav said... "if it is bijective"....u must take it as bijective....their objective is to make urself calculate the inverse....n thts it...

Scorching goIITian

Joined: 23 Mar 2009
Posts: 293
20 Apr 2009 14:40:04 IST
1 people liked this

domain shud be mentioned otherwise assume it as bijective

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
20 Apr 2009 19:16:21 IST
1 people liked this

what are u saying... i cant get it brother...

they clearly mentioned the domain and codomain to be R.

But we can clearly see that the function is bijective if and only if the codomain is [ -1,  )

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
20 Apr 2009 19:17:48 IST
1 people liked this

why should we assume ???

what are u saying... i cant get it brother...

they clearly mentioned the domain and codomain to be R.

But we can clearly see that the function is bijective if and only if the codomain is [ -1,  )

Blazing goIITian

Joined: 1 Apr 2007
Posts: 1084
21 Apr 2009 11:10:50 IST
0 people liked this

ya...true to maths its a wrong ques. but why u r taking so much tension over tht thing.... they just want to know whether u know how to find inverse or not...well we r getting free salutes :D :)

Blazing goIITian

Joined: 5 Jun 2007
Posts: 978
21 May 2009 08:25:31 IST
0 people liked this

this question came in aieee 09... gr8 ...

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 10050 m Post - 2205
4. edison
 Altitude - 10815 m Post - 7802
5. Sagar Saxena
 Altitude - 8625 m Post - 8064
 Altitude - 6330 m Post - 1979

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone