Hey there Sign in to join this conversationNew here? Join for free

how to show a function is invertible

Announcements Posted on
    • Thread Starter
    • 0 followers
    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
    • 7 followers
    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)
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    no not really...
    • 10 followers
    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.
    • Thread Starter
    • 0 followers
    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?
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    ignore that, thanks
    • 10 followers
    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?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  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 the button to the right to create your account

    Slide to join now Processing…

Updated: September 10, 2008
New on TSR

Student crowdfunds degree

Graduate raises £26,000 online for Masters course

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.