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

Why does the function x^2 not have an inverse? Watch

    • Thread Starter
    Offline

    11
    ReputationRep:
    ^Basically what the title says.
    • Community Assistant
    Offline

    11
    ReputationRep:
    (Original post by sabahshahed294)
    ^Basically what the title says.
    f(x) = x^2 is not a one-to-one function, meaning for each f(x) value there are more than one possible x value.
    Offline

    10
    ReputationRep:
    (Original post by sabahshahed294)
    ^Basically what the title says.
    only bijective functions have inverses. However, it is possible to turn functions that are not bijective into bijective functions by tweaking the domain.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by SherlockHolmes)
    f(x) = x^2 is not a one-to-one function, meaning for each f(x) value there are more than one possible x value.
    So, only functions which are one-to-one functions have inverses?

    (Original post by Naruke)
    only bijective functions have inverses. However, it is possible to turn functions that are not bijective into bijective functions by tweaking the domain.
    If you don't mind but can you explain how?
    • Community Assistant
    Offline

    11
    ReputationRep:
    (Original post by sabahshahed294)
    So, only functions which are not one-to-one functions have inverses?



    If you don't mind but can you explain how?
    No. Only one-to-one functions have inverses.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by SherlockHolmes)
    No. Only one-to-one functions have inverses.
    Yeah, edited my post. Sorry I misread your post at first.
    Offline

    3
    ReputationRep:
    (Original post by sabahshahed294)
    ^Basically what the title says.
    Only one-to-one functions have inverses, as the inverse of a many-to-one function would be one-to-many, which isn't a function.

    x^2 is a many-to-one function because two values of x give the same value
    e.g. both 3 and -3 map to 9

    Hope this helps
    Offline

    13
    ReputationRep:
    You can have f(x) = x^2 to be a one-to-one function if you restrict the domain as mentioned.

    For example: f(x) = x^2, x ≥ 0 or f(x) = x^2, x ≤ 0. This means you'll half of the U shaped graph so it now becomes a one-to-one function
    • Community Assistant
    Offline

    11
    ReputationRep:
    (Original post by sabahshahed294)
    So, only functions which are one-to-one functions have inverses?
    So yes this is now correct.
    Offline

    3
    ReputationRep:
    (Original post by sabahshahed294)
    So, only functions which are one-to-one functions have inverses?



    If you don't mind but can you explain how?
    basically the idea is the inverse of y=x^2 would have to be x=+/-sqrt(y) (which is multivalued so not a function), so if we restrict ourselves to the right-hand side of the original parabola (where x>=0), we get x=sqrt(y), and if we instead look just at the left-hand side (where x<0), we get x=-sqrt(y).
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by ntada99)
    Only one-to-one functions have inverses, as the inverse of a many-to-one function would be one-to-many, which isn't a function.

    x^2 is a many-to-one function because two values of x give the same value
    e.g. both 3 and -3 map to 9

    Hope this helps
    Yeah, got the idea. Thank you.

    (Original post by ManLike007)
    You can have f(x) = x^2 to be a one-to-one function if you restrict the domain as mentioned.

    For example: f(x) = x^2, x ≥ 0 or f(x) = x^2, x ≤ 0. This means you'll half of the U shaped graph so it now becomes a one-to-one function
    Understood. Thanks

    (Original post by SherlockHolmes)
    So yes this is now correct.
    Thank you

    (Original post by HapaxOromenon3)
    basically the idea is the inverse of y=x^2 would have to be x=+/-sqrt(y) (which is multivalued so not a function), so if we restrict ourselves to the right-hand side of the original parabola (where x>=0), we get x=sqrt(y), and if we instead look just at the left-hand side (where x<0), we get x=-sqrt(y).
    Thank you, got it now!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

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