Find a rational function f:RR\rightarrow RR with range f(RR)=[0,1] (Thus

Gary Johnson

Gary Johnson

Answered question

2022-02-18

Find a rational function f:RR with range f(R)=[0,1] (Thus f(x)=P(x)Q(x) for all xR for suitable polynomials P and Q, where Q has no real root).
I have no clue where to begin.

Answer & Explanation

chung001vba

chung001vba

Beginner2022-02-19Added 6 answers

The image of the rational function xx1+x2 is a compact interval. Compose it with a suitable affine function to obtain a rational function with image [0,1].

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