A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
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.
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.

This Question is Open

littmo12
 2 years ago
Best ResponseYou've already chosen the best response.0could you explain it please? thankyou!

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2i 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

scarydoor
 2 years ago
Best ResponseYou've already chosen the best response.0the first response isn't a rational function. They have to be polynomials.

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2oh what @scarydoor said

scarydoor
 2 years ago
Best ResponseYou've already chosen the best response.0@satellite73 's hint is on the money... easy to convert that to the right function.

littmo12
 2 years ago
Best ResponseYou've already chosen the best response.0@scarydoor how can i convert it to the right function? i dont understand

littmo12
 2 years ago
Best 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...

scarydoor
 2 years ago
Best ResponseYou've already chosen the best response.0Satellite'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].

littmo12
 2 years ago
Best ResponseYou've already chosen the best response.0ahh thankyou! yes it makes sense
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.