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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.

  • 2 years ago
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  1. mahmit2012 Group Title
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    x+1/absx+2

    • 2 years ago
  2. littmo12 Group Title
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    could you explain it please? thankyou!

    • 2 years ago
  3. satellite73 Group Title
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    you could try something like \[f(x)=\frac{x}{x^2+1}\]

    • 2 years ago
  4. satellite73 Group Title
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    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

    • 2 years ago
  5. scarydoor Group Title
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    the first response isn't a rational function. They have to be polynomials.

    • 2 years ago
  6. satellite73 Group Title
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    only problem with @mahmit answer is \(|x+2|\) is not a polynomial

    • 2 years ago
  7. satellite73 Group Title
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    oh what @scarydoor said

    • 2 years ago
  8. scarydoor Group Title
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    @satellite73 's hint is on the money... easy to convert that to the right function.

    • 2 years ago
  9. littmo12 Group Title
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    @scarydoor how can i convert it to the right function? i dont understand

    • 2 years ago
  10. littmo12 Group Title
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    \[f(x)=\frac{ x+1 }{ x^2+1 }\] can anyone confirm this answer? i think its right...

    • 2 years ago
  11. littmo12 Group Title
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    @satellite73

    • 2 years ago
  12. scarydoor Group Title
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    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].

    • 2 years ago
  13. littmo12 Group Title
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    ahh thankyou! yes it makes sense

    • 2 years ago
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