problem with an inequation

[Lamis]

Hi, im having a problem sloving this question
f(x)=(sqrt(x^2+1)+x)/(x^2+1) if x>0
f(X)=x^3+2x+1 if x<0
I have to prove that for any x>0: 0<=f(x)<=(2x+1)/(x^2+1)

 

[Dr.Peterson]

Hi, i'm having a problem solving this question
f(x)=(sqrt(x^2+1)+x)/(x^2+1) if x>0
f(x)=x^3+2x+1 if x<0
I have to prove that for any x>0: 0<=f(x)<=(2x+1)/(x^2+1)

What you're given is a piecewise-defined function.

You are asked to prove an inequality that applies only to the first (positive x) case.

So show us what ideas you have: If x>0, how might you show that 0 <= (sqrt(x^2+1)+x)/(x^2+1) <= (2x+1)/(x^2+1) ?

Keep this in mind:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com

 

[lev888]

Hi, im having a problem sloving this question
f(x)=(sqrt(x^2+1)+x)/(x^2+1) if x>0
f(X)=x^3+2x+1 if x<0
I have to prove that for any x>0: 0<=f(x)<=(2x+1)/(x^2+1)

If you didn't understand my replies on facebook you could've asked for a clarification instead of just posting the problem somewhere else.