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littmo12

  • 2 years ago

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.

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

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

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

  4. satellite73
    • 2 years ago
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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

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

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

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

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

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

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

  11. littmo12
    • 2 years ago
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    @satellite73

  12. scarydoor
    • 2 years ago
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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].

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

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