Sunday

December 21, 2014

December 21, 2014

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

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 9:39pmFirst, 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 11:48pmIDK!!!

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 + ...

Math - I'm trying to use DeMoirre's Theorem to compute and express this in ...

statistics - mu=78 population std deviation=12 Normal Distribution n=16 alpha ...

math - the number of ways in which 18 students in Mr. Garr grade 3 class can ...

math - The weights (in pounds) of a sample of five boxes being sent by UPS are: ...

math - find the greatest common factor and simplify your answer. 4v to the 7th ...

math - simplify, 4v to the 7th power y to the 9th power and 16v to the 6th power...

math - 4v to the 7th power y to the 9th power and 16v to the 6th power x to the ...