Turn on thread page Beta
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by _gcx)
    Bit late to the party, but for the sake of aesthetics, you can write this as,

    \csc^2 x\left(x^5+8x^4 - 9x^2 - 2\right)

    From which you can observe the function as being many to one through the periodicity of \sin.
    woah, what's this csc? i feel a bit stupid since im doing uni level and i still don't get it
    Offline

    18
    ReputationRep:
    (Original post by will'o'wisp2)
    woah, what's this csc? i feel a bit stupid since im doing uni level and i still don't get it
    it's just \frac 1 {\sin x}, sorry if that was unclear
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by _gcx)
    it's just \frac 1 {\sin x}, sorry if that was unclear
    Ah right, so it's a sin graph with the function of the stuff int he brackets then?
    Offline

    13
    ReputationRep:
    (Original post by _gcx)
    No, I intended it to be read as \csc^2(x) \times \ldots . My approach is more heuristic so if you're still confused, investigating turning points per the other posts is probably the way to go.
    I personally don't see how you could easily tell that a function in the form f(x)=\csc^2(x)g(x) is necessarily many to one. Could you elaborate?
    Offline

    18
    ReputationRep:
    (Original post by I hate maths)
    I personally don't see how you could easily tell that a function in the form f(x)=\csc^2(x)g(x) is necessarily many to one. Could you elaborate?
    Looking back, I have no idea where I was going with that either, I probably wasn't paying much attention. I've added,


    Edit: I have no idea where I was going with this. I should've really explained why the second term is not one-to-one, ie. x^5 + 8x^4 - 9x^2 - 2 is not one-to-one as its derivative is neither strictly positive nor strictly negative, then perhaps using the product rule to conclude that the function \csc^2 x\left(x^5+8x^4 - 9x^2 - 2\right) is not one-to-one.

    Basically, a continuous function f is one-to-one if its derivative is strictly positive or strictly negative.
    Offline

    22
    ReputationRep:
    (Original post by _gcx)
    Basically, a continuous function f is one-to-one if its derivative is strictly positive or strictly negative.
    A continuous function need not have a derivative.
    Offline

    18
    ReputationRep:
    (Original post by Zacken)
    A continuous function need not have a derivative.
    Indeed, should I say, a continuous, differentiable function.
    Offline

    22
    ReputationRep:
    (Original post by _gcx)
    Indeed, should I say, a continuous, differentiable function.
    If a function is differentiable, it is automatically continuous - so there is no need to specify continuity.

    NB: there wasn't anything technically wrong with your statement -- it just read weirdly because of the aforementioned.

    [Also, you have sufficiency but not necessity, for example x^3 is differentiable and bijective, but has 0 derivative at 0]
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 7, 2017
Poll
Do you think parents should charge rent?
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

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

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