You are Here: Home >< Maths

# how to show a function is invertible Watch

1. 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. 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. no not really...
4. If the function is strictly increasing then whenever . You should be able to see that this implies the function is also injective.
5. (Original post by Kolya)
If the function is strictly increasing then whenever . So, clearly, cannot equal whenever . 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. ignore that, thanks
7. 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.)

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.

This forum is supported by:
Today on TSR

### Stuck for things to do this summer?

Come and get some inspiration.

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources

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

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