Solving f°f: The Mystery of the Answer

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The discussion revolves around finding the composition of the function f°f, where f(x) = x/(x+1). Initially, there was confusion regarding the correct simplification of the function, leading to an incorrect intermediate result. Clarification was sought on the division of complex fractions, specifically the need to find a common denominator rather than simply multiplying by the reciprocal. After reviewing a tutorial, the correct answer of f°f = x/(2x+1) was achieved by applying the appropriate method. The conversation highlights the importance of understanding fraction operations in function composition.
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Homework Statement



Find f°f

Homework Equations



f(x)=x/x+1

The Attempt at a Solution



\frac{x}{x+1} divided by \frac{x}{x+1} I got \frac{1}{x+1}+1 but I know the answer in the book is \frac{x}{2x+1}. I'm not sure how the book arrived at that answer.
 
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How did you get your result?
 
najatau said:

Homework Statement



Find f°f

Homework Equations



f(x)=x/x+1
You mean f(x) = x/(x+1), right? Because what you wrote simplifies to f(x)=2 for x≠0.

The Attempt at a Solution



\frac{x}{X+1}divided by\frac{x}{x+1}
Are X and x supposed to be the same variable? If not, what's X? If they're supposed to be the same, use the same letter.

How did you come up with that division? Please explain what you're doing in more detail.

I got \frac{1}{x+1}+1 but I know the answer in the book is \frac{x}{2x+1}. I'm not sure how the book arrived at that answer.
 
Thanks for responding. I just found out why I got the wrong answer. I wasn't dividing complex/compound fractions with monomials in the denominator correctly. I tried to multiply the numerator by the reciprocal of the denominator instead of finding the lowest common denominator for the numerator and denominator like I saw in this video.

I got the book's answer when I did it the way the video instructed. Not sure why I didn't get the same answer either way.
(:-/
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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