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littmo12
Group Title
Find a rational function f:R> with range f(R)=[1,1]. (Thus f(x)=P(x)/Q(x) for all xeR for suitable polynomials P and Q where Q has no real root.
 one year ago
 one year ago
littmo12 Group Title
Find a rational function f:R> with range f(R)=[1,1]. (Thus f(x)=P(x)/Q(x) for all xeR for suitable polynomials P and Q where Q has no real root.
 one year ago
 one year ago

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mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
x+1/absx+2
 one year ago

littmo12 Group TitleBest ResponseYou've already chosen the best response.0
could you explain it please? thankyou!
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
you could try something like \[f(x)=\frac{x}{x^2+1}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
i mean to say something "like" it. that one doesn't work because the range of \[f(x)=\frac{x}{x^2+1}\] is \([\frac{1}{2},\frac{1}{2}]\) you will have to adjust it
 one year ago

scarydoor Group TitleBest ResponseYou've already chosen the best response.0
the first response isn't a rational function. They have to be polynomials.
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
only problem with @mahmit answer is \(x+2\) is not a polynomial
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
oh what @scarydoor said
 one year ago

scarydoor Group TitleBest ResponseYou've already chosen the best response.0
@satellite73 's hint is on the money... easy to convert that to the right function.
 one year ago

littmo12 Group TitleBest ResponseYou've already chosen the best response.0
@scarydoor how can i convert it to the right function? i dont understand
 one year ago

littmo12 Group TitleBest ResponseYou've already chosen the best response.0
\[f(x)=\frac{ x+1 }{ x^2+1 }\] can anyone confirm this answer? i think its right...
 one year ago

littmo12 Group TitleBest ResponseYou've already chosen the best response.0
@satellite73
 one year ago

scarydoor Group TitleBest ResponseYou've already chosen the best response.0
Satellite's function is almost right, in that the range is [1/2, 1/2]. But you want it [1,1]. So you want to stretch it out to that. If you multiply the function by 2, then if you think about it a bit, you'll see that the range will be [1,1].
 one year ago

littmo12 Group TitleBest ResponseYou've already chosen the best response.0
ahh thankyou! yes it makes sense
 one year ago
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