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Set Theory: prove f(x)= x ÷ sqrt[x^2+1] is Bijec. on (-1, 1)  TOPIC_SOLVED

Was hoping I could get some help showing the steps of this problem.

Prove that the following is a bijection.
range (-1,1) f(x)= x ÷ sqrt [ (x^2) + 1 ]
by itscomplicated
on Fri Jul 16, 2010 8:10 pm
 
Forum: Discrete Math
Topic: Set Theory: prove f(x)= x ÷ sqrt[x^2+1] is Bijec. on (-1, 1)
Replies: 5
Views: 4517

Re: Set Theory: prove f(x)= x ÷ sqrt[x^2+1] is Bijec. on (-1  TOPIC_SOLVED

Definition of a Bijection is that the function must be Injective AND surjective and therefore it is Bijective. Did you need to know the definition or are you asking if I even know it? as for my steps I am not quite clear how to approach it and the only help I have gotten so far is that since it is a...
by itscomplicated
on Sat Jul 17, 2010 1:23 am
 
Forum: Discrete Math
Topic: Set Theory: prove f(x)= x ÷ sqrt[x^2+1] is Bijec. on (-1, 1)
Replies: 5
Views: 4517

Re: Set Theory: prove f(x)= x ÷ sqrt[x^2+1] is Bijec. on (-1  TOPIC_SOLVED

The book the teacher assigned to my class simply is a different method of approaching proofs than most (it literally says it). Anyways one of the ways to approach the problem was to say, Assume there is an x sub 1 in f(x) and another x sub 2 in f(x) you can then prove they are equal thus proving tha...
by itscomplicated
on Sun Jul 18, 2010 2:15 am
 
Forum: Discrete Math
Topic: Set Theory: prove f(x)= x ÷ sqrt[x^2+1] is Bijec. on (-1, 1)
Replies: 5
Views: 4517

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