When

f(x)=x^7+2x^3+x-1

I have found

f^-1(3)=1

But I need to prove this.

Can anyone help?

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- Jul 24th 2011, 12:18 AMArroninverse functions
When

f(x)=x^7+2x^3+x-1

I have found

f^-1(3)=1

But I need to prove this.

Can anyone help? - Jul 24th 2011, 12:23 AMFernandoRevillaRe: inverse functions
and is strictly increasing.

- Jul 24th 2011, 01:25 AMArronRe: inverse functions
I need to find f^-1, or the inverse of f. Not sure how to do this?

- Jul 24th 2011, 02:38 AMFernandoRevillaRe: inverse functions
- Jul 24th 2011, 02:58 AMmr fantasticRe: inverse functions
- Jul 24th 2011, 11:56 AMchisigmaRe: inverse functions
If finding is a 'categoric imperative' , then a method based on advanced tecniques of complex analysis will be supplied without demonstration...

If the function the inverse of which has to be found is...

(1)

... then first with the variable substitution we obtain...

(2)

Now the inverse of a function for which is can be written in series expansion as...

(3)

... where the are given by...

(4)

In our case of course is...

(5)

... and the x as function of y will be...

(6)

Details of computation of the are left to the [young I suppose...] starter of the thread...

Kind regards

- Jul 25th 2011, 12:58 PMArronRe: inverse functions
Thanks for your help everyone.

One final thing, I am trying to determine the value of (f^-1)'(3)

Would this = 1/f'(3) = -1 - Jul 25th 2011, 02:36 PMFernandoRevillaRe: inverse functions
- Jul 27th 2011, 01:04 PMArronRe: inverse functions
would that be 1/13.

- Jul 27th 2011, 01:49 PMFernandoRevillaRe: inverse functions
- Jul 27th 2011, 03:25 PMmr fantasticRe: inverse functions