Composition of Functions

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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.
 

Answers and Replies

  • #2
PeroK
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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.
What is ##f(f(-1)##?
 
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  • #3
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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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  • #4
Ray Vickson
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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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