Hey! Sign in to get help with your study questionsNew here? Join for free to post

how to show a function is invertible

Announcements Posted on
At uni? What do you think of the careers support? 12-02-2016
How proud of your uni are you? Take our survey for the chance to win a holiday! 09-02-2016
  1. Offline

    ReputationRep:
    say f(x)=(4x^3)/((x^2) + 1)

    how can i show f has an inverse?

    i understand that for a function to be invertible, f(x1) does not equal f(x2) whenever x1 does not equal x2. but im unsure how i can apply it to the above function. help please, thanks
  2. Offline

    ReputationRep:
    Well, there are many ways to prove that a function is injective and hence has the inverse you seek. One of them is to show that the function is increasing (Can you see why)
  3. Offline

    ReputationRep:
    no not really...
  4. Offline

    If the function is strictly increasing then f(x_2) > f(x_1) whenever x_2 > x_1. You should be able to see that this implies the function is also injective.
  5. Offline

    ReputationRep:
    (Original post by Kolya)
    If the function is strictly increasing then f(x_2) > f(x_1) whenever x_2 > x_1. So, clearly, f(x_1) cannot equal f(x_2) whenever x_1 \neq x_2. Hence strictly increasing means the function is injective.
    oh i get it now, but is that enough proof? would i need to give some values or something?
  6. Offline

    ReputationRep:
    ignore that, thanks
  7. Offline

    Within the context of the question, I think it would be enough to just state that strictly increasing implies injective, and then use that idea to complete the question. (However, the proof of the intermediate result is easy.)

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: September 10, 2008
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Today on TSR

Find out who won!

TSR community awards 2015

Poll
Would you be influenced by unis giving flexible offers (so you can miss by a grade)?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read here first

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.