What is the domain of f(f(x)) for f(x)= x/(1+x)?

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Homework Help Overview

The problem involves the function f(x) = x/(1+x) and seeks to determine the composition f(f(x)) as well as its domain. Participants are exploring the implications of the function's definition and the resulting domain constraints.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to find f(f(x)) and its domain, with some expressing confusion over their results. There is a focus on identifying mistakes in the domain calculation and understanding the implications of undefined values.

Discussion Status

The discussion is ongoing, with participants sharing their findings and questioning the correctness of their domain conclusions. Some have suggested a revised domain based on the realization of undefined values, while others are still clarifying their reasoning.

Contextual Notes

Participants are considering the intersection of multiple domains derived from the function's properties and are grappling with the implications of certain values leading to undefined results.

Jpyhsics
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Homework Statement


f(x)= x/(1+x)

What is f(f(x)) and what is its domain.

2. The attempt at a solution
I found f(f(x))= x/(1+2x)
and the domain: (-∞,-1/2)∪(-1/2,∞) , but it is saying that I have the wrong domain. What mistake have I made?


My process for finding domain:
1. Find the domain of f : x≠-1
2. Use the definition D: {x∈(-∞,-1)∪(-1,∞) | (x/1+x) ≠ -1}
3. Find the ∩ (intersection) for the two domains.
 
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Jpyhsics said:

Homework Statement


f(x)= x/(1+x)

What is f(f(x)) and what is its domain.

2. The attempt at a solution
I found f(f(x))= x/(1+2x)
and the domain: (-∞,-1/2)∪(-1/2,∞) , but it is saying that I have the wrong domain. What mistake have I made?


My process for finding domain:
1. Find the domain of f : x≠-1
2. Use the definition D: {x∈(-∞,-1)∪(-1,∞) | (x/1+x) ≠ -1}
3. Find the ∩ (intersection) for the two domains.

What is ##f(f(-1)##?
 
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Likes   Reactions: SammyS
PeroK said:
What is ##f(f(-1)##?
Oh I see! Its undefined!
So I guess my domain should be (-∞,-1)∪(-1,-1/2)∪(-1/2,∞)

Thank You!
 
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Likes   Reactions: Delta2
Jpyhsics said:
Oh I see! Its undefined!
So I guess my domain should be (-∞,-1)∪(-1,-1/2)∪(-1/2,∞)

Thank You!

Formally: if ##D_1 = A \cup B## and ##D_2 = C \cup D## then $$ D_1 \cap D_2 = (A\cap C) \cup (A \cap D) \cup (B \cap A) \cup (B \cap D)$$ Apply this to ##A = (-\infty,-1),## ##B = (-1,\infty)##, ##C = (-\infty, -1/2)## and ##D = (-1/2,\infty).##
 

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