Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
 You are Here: Home >< Maths

# Inverse functions. watch

1. Can anyone help solve this problem:

Explain why the graph of f(x) = (x^2 + 1)/(x^2 - 1) and its inverse function f-1(x) is also a solution to x^3 - x^2 - x -1 = 0. Show that an approximate solution is x=1.84.
Attached Images

2. Why you doing math

Posted from TSR Mobile
3. Use whatever you got for f-1(x) and set it equal to f(x), and then just rearrange.
4. (Original post by tommy_lees)
Can anyone help solve this problem:

Explain why the graph of f(x) = (x^2 + 1)/(x^2 - 1) and its inverse function f-1(x) is also a solution to x^3 - x^2 - x -1 = 0. Show that an approximate solution is x=1.84.
Where have you got to so far?
5. Since they never tell you to explicitly find the inverse function, this is what I believe they want you to do:

As you probably got from your sketch earlier, the inverse function is a reflection of the original function in the line y=x. Now for a point of intersection between both curves (what you are looking for in f(x) = f^-1 (x)) said point has to lie on both curves. Any idea on where else the point must lie? (once you figure this out, it is a simple rearrangement).
6. Moved thread to Maths forum as more likely to get answers here, not that you haven't already gotten some
7. (Original post by Solivagant)
Use whatever you got for f-1(x) and set it equal to f(x), and then just rearrange.

Thanks I did that, i set f(x) = f-1(x).

I got:

x^4 -2x^3 + 1 = 0

This has the correct solution of 1.84 when solved but I don't see how it relates to x^3 - x^2 - x -1 = 0

8. (Original post by tommy_lees)
Thanks I did that, i set f(x) = f-1(x).

I got:

x^4 -2x^3 + 1 = 0

This has the correct solution of 1.84 when solved but I don't see how it relates to x^3 - x^2 - x -1 = 0

Work out a factor of x^4 - 2x^3 + 1 = 0 and then if you use long division by that factor you should get that
(Factor)*(x^3 - x^2 - x -1)=0 therefore you have either one of the two factors will equal zero and that's how it relates

Hint: Factor
Spoiler:
Show
When x=1 then the equation holds true, so divide x^4 - 2x^3 +1 by x-1 to get the other factor.
9. (Original post by MathsNerd1)
Work out a factor of x^4 - 2x^3 + 1 = 0 and then if you use long division by that factor you should get that
(Factor)*(x^3 - x^2 - x -1)=0 therefore you have either one of the two factors will equal zero and that's how it relates

Hint: Factor
Spoiler:
Show
When x=1 then the equation holds true, so divide x^4 - 2x^3 +1 by x-1 to get the other factor.
Ah ok thank you
10. (Original post by tommy_lees)
Ah ok thank you
Happy to help
11. (Original post by tommy_lees)
.
I know you've managed to succeed with your question, but a way to get it out without long-division is to see that all solutions to f^-1(x) = f(x) is the same as the solutions of the intersections of the line y=x and f(x) i.e. x = f(x), rearrange the equation and you get your relation instantly!

(That was the hint I posted above)

Reply
Submit reply
Turn on thread page Beta
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:
Updated: July 1, 2014
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

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

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.