Compositions, Inverses and Combinations of Functions

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Discussion Overview

The discussion revolves around finding a formula for the function p(x) given the composition p(q(x))=2/(5+x) and q(x)=1+x. The scope includes mathematical reasoning and problem-solving related to function compositions and inverses.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant seeks assistance in solving the problem of finding p(x) based on the given compositions.
  • Another participant suggests defining a new function f(q(x)) and replacing instances of x with 1 + x to derive the original function f(x).
  • A participant expresses difficulty in understanding the topic and requests a step-by-step explanation.
  • A hint is provided that involves solving for a variable a in the equation a + 1 + x = 5 + x to find p(x).
  • A later reply indicates that the participant has arrived at the conclusion that p(x)=2/(4+x) after following the hints provided.

Areas of Agreement / Disagreement

The discussion shows a progression towards a solution, with one participant confirming their understanding and arriving at a proposed formula for p(x). However, the initial request for help indicates that there may be varying levels of understanding among participants.

Contextual Notes

The discussion does not clarify all assumptions or steps involved in deriving p(x), and the final formula presented may depend on interpretations of the hints given.

Who May Find This Useful

Students struggling with function compositions and inverses, as well as those seeking collaborative problem-solving approaches in mathematics.

mak23
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HELP!

given p(q(x))=2/(5+x) and q(x)=1+x . find a formula for p(x).

Someone please help. I don't know how to do this problem .Thanks in advance
(PS: would be really helpful if solution is also given)
 
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Hi mak23,

Since the denominator of p(x) contains the only instance of x, let's define a new function f(q(x)) = f(1 + x) = 5 + x.
So we start with our function f(x) and replace each instance of x with 1 + x. What is our original function f(x)?

Does that help?
 
Hi greg1313,

Thanks for replying to my post. I'm really terrible in this chapter. If u could explain step by step, I would understand much better and quickly. I'm sorry if I'm troubling u.
 
No problem. :)

Here's a hint: a + 1 + x = 5 + x. What is a? What, then, is p(x)?
 
ahaaa...Now i get it..

So p(x)=2/(4+x)

Thank you so much greg1313 for the help!
 

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