Home » Ask & Discuss » Mathematics. » Differential Calculus « Back to Discussion

Differential Calculus

Cool goIITian

Joined:	6 Sep 2007
Post:	73

18 Sep 2007 22:31:32 IST

0 People liked this

390

Question on Functions

None

Q 1 Which of the following functions from Z to itself are bijections ?

a ) f (x) = x^3

b ) f (x) = x + 2

c ) f (x) = 2x + 1

d ) f (x) = x^2 + x

Q 2 Let f : A to B & g : B to C be bijections, then ( fog )^(inv) =

a ) f(inv) og(inv)

b ) fog

c ) g(inv) of (inv)

d ) gof

Share this article on:

Comments (2)

Anshuman Johri

Blazing goIITian

Joined: 27 Jan 2007

Posts: 559

18 Sep 2007 22:43:08 IST

Like 0 people liked this

Ans1> b,c

Manasi

Forum Expert

Joined: 1 Dec 2006

Posts: 2108

18 Sep 2007 22:51:52 IST

Like 3 people liked this

for a function to be bijective..it should be one-one onto....

now a function will be one-one and onto...if and only if...its monotonic... either increasing or decreasing..... u can easily find such function by plotting its graph...

here.... 2nd and 3rd will be monotonic in nature...so they r bijective functions

Quick Reply

Reply

	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