Re: Can we find the function?

matt271829-news@xxxxxxxxxxx writes:

On Oct 31, 7:13 pm, "G. A. Edgar" <ed...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article <1193840751.971164.78...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





polymedes <polyme...@xxxxxxxxx> wrote:
On Oct 31, 2:44 pm, David W. Cantrell <DWCantr...@xxxxxxxxxxx> wrote:
polymedes <polyme...@xxxxxxxxx> wrote:
On Oct 31, 1:55 pm, David W. Cantrell <DWCantr...@xxxxxxxxxxx>
wrote:
polymedes <polyme...@xxxxxxxxx> wrote:
Let (f o f)(x) = -2x + 3

Can we find the original function f ?

How about f(x) = Sqrt(-2) x + 1 - Sqrt(-2) ?

(Of course, I'm not saying that is the only such function.)

David

Can we answer this question instead: Is it possible for the
composition of two non-polynomial functions, to be a polynomial
function?

Sure: log(exp(x)) = x.

David

Ok, you're right, but let me change my question. Can the composition
of a non-polynomial function with itself be a polynomial, excluding
monomials?

f(x) = x^sqrt(2), f(f(x)) = ?


He said "excluding monomials".

OK then: f(x) = floor(x) + 1 + sqrt(frac(x)) if floor(x) is even
= floor(x) + 1 + frac(x)^2 if floor(x) is odd
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

Relevant Pages

  • Re: Can we find the function?
    ... composition of two non-polynomial functions, ... He said "excluding monomials". ...
    (sci.math)
  • Re: Can we find the function?
    ... composition of two non-polynomial functions, ... of a non-polynomial function with itself be a polynomial, excluding ...
    (sci.math)
  • Re: Can we find the function?
    ... composition of two non-polynomial functions, ... of a non-polynomial function with itself be a polynomial, excluding ...
    (sci.math)
  • Re: Can we find the function?
    ... polymedes wrote: ... composition of two non-polynomial functions, ...
    (sci.math)
  • Re: Can we find the function?
    ... composition of a non-polynomial function with itself be a ... polynomial, excluding monomials? ... f) = x, certainly a polynomial function. ...
    (sci.math)