Posted by **Suzy** on Sunday, November 28, 2010 at 5:30pm.

For 0 < x < 1, let

f(x) = (1 + x)(1 + x4)(1 + x16)(1 + x64)(1 + x256) · · ·

Compute f to the power of -1 times 8 divided by 5 times f times 3/8

- Math -
**MathMate**, Sunday, November 28, 2010 at 9:39pm
First, we have to establish that the function f(x) is invertible on the interval [0,1].

f(x) consists of a polynomial with all positive terms, so it is strictly increasing and consequently one-to-one and onto. Thus f^{-1}(x) exists.

Where x can be solved explicitly for y, an analytic expression of the inverse can be found. In other cases, we can resort to numerical solutions, which can be obtained to any accuracy we wish. For the given problem, we will supply a numerical solution.

We start with a property of f^{-1}(x). which can be looked at as

f^{-1}(f(x)) = x for all x on the given interval.

Thus f^{-1}(f(3/8))= 3/8.

To find y=f^{-1}(8/5f(3/8)), we need to find y for which

f(y)=8/5f(3/8)

then

f^{-1}(f(y))

=f^{-1}(85f(3/8))

=y

We can find the approximation by the secant method.

First evaluate

8/5f(3/8)

=2.243506202480352

Knowing f(0)=1, f(1)=32,

we give a first approximation of

y0=0.7

f(0.7)=2.115

f(0.8)=2.609

The new y could be interpolated:

y1=0.7+(0.8-0.7)*(2.2435-2.115)/(2.609-2.115)

=0.72602

We get successively

y2=0.73172

y3=0.73179

....

y=0.7317902526225

Check:

f(y)=2.243506202480352 OK

Therefore:

f^{-1}(8/5f(3/8))=0.7317902526225

- Math -
**Freaky**, Sunday, November 28, 2010 at 11:48pm
IDK!!!

but the answer above needs to be put in simpler words to understand it

## Answer this Question

## Related Questions

- math - For 0 < x < 1, let f(x) = (1 + x)(1 + x4)(1 + x16)(1 + x64)(1 + ...
- math - For 0 < x < 1, let f(x) = (1 + x)(1 + x4)(1 + x16)(1 + x64)(1 + ...
- math - For 0 < x < 1, let f(x) = (1 + x)(1 + x4)(1 + x16)(1 + x64)(1 + ...
- algerbra - how do i set up and whats the prosedure to solve 10 to the 7th power ...
- Math - A few here. 4x-8 ------ x(squared)-4 _________________________ 2m(squared...
- algebra2 plzz help - how do you solve these problems (5x)to the power of a+4(5x)...
- math - log [ a^3\/ab / (ab^2) ] --> in words this is, log(a to the power 3 ...
- math - please solve 100 divided by 5 to the 2nd power times 4 to the 3rd power.
- Algebra - What is the value of x. 2x times 2 to the 4th power divided by 2 to ...
- Math - I need help with these questions: Copy the equations. Add brakcets to ...

More Related Questions