anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
x+1/absx+2
anonymous
  • anonymous
could you explain it please? thankyou!
anonymous
  • anonymous
you could try something like \[f(x)=\frac{x}{x^2+1}\]

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anonymous
  • anonymous
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
anonymous
  • anonymous
the first response isn't a rational function. They have to be polynomials.
anonymous
  • anonymous
only problem with @mahmit answer is \(|x+2|\) is not a polynomial
anonymous
  • anonymous
oh what @scarydoor said
anonymous
  • anonymous
@satellite73 's hint is on the money... easy to convert that to the right function.
anonymous
  • anonymous
@scarydoor how can i convert it to the right function? i dont understand
anonymous
  • anonymous
\[f(x)=\frac{ x+1 }{ x^2+1 }\] can anyone confirm this answer? i think its right...
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
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].
anonymous
  • anonymous
ahh thankyou! yes it makes sense

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