## anonymous 3 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. anonymous

x+1/absx+2

2. anonymous

could you explain it please? thankyou!

3. anonymous

you could try something like $f(x)=\frac{x}{x^2+1}$

4. 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

5. anonymous

the first response isn't a rational function. They have to be polynomials.

6. anonymous

only problem with @mahmit answer is $$|x+2|$$ is not a polynomial

7. anonymous

oh what @scarydoor said

8. anonymous

@satellite73 's hint is on the money... easy to convert that to the right function.

9. anonymous

@scarydoor how can i convert it to the right function? i dont understand

10. anonymous

$f(x)=\frac{ x+1 }{ x^2+1 }$ can anyone confirm this answer? i think its right...

11. anonymous

@satellite73

12. 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].

13. anonymous

ahh thankyou! yes it makes sense