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

AI Thread Summary
The function f(x) = x/(1+x) leads to f(f(x)) = x/(1+2x). The initial domain found was incorrect; the correct domain is (-∞,-1)∪(-1,-1/2)∪(-1/2,∞). The mistake was in not accounting for the values that make f(f(x)) undefined, specifically when x = -1/2. The intersection of the domains must be carefully calculated to ensure all restrictions are considered. Understanding these domain restrictions is crucial for accurately determining the function's behavior.
Jpyhsics
Messages
84
Reaction score
2

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.
 
Physics news on Phys.org
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)##?
 
  • Like
Likes 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!
 
  • Like
Likes 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).##
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

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
View full post »

Thread 'Greatest possible value of a constant in polynomial'

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
View full post »

Similar threads

Find the domain and the range of ##f-3g##
Replies
3
Views
2K
Finding the domain of a composite function
Replies
10
Views
2K
F(x)=(x+1)^0.5, h(x)=x^2+3, what is the range of f(h(x))?
Replies
4
Views
1K
To find the range of a given ##\sin## function
Replies
15
Views
2K
Determining the domain and range for the function ##f^{-1}##
Replies
2
Views
1K
Composite and Inverse Functions Problem
Replies
3
Views
2K
What are the implied domain and range of cos(arctan(x))?
Replies
3
Views
2K
To find the boundedness of a given function
Replies
14
Views
3K
Understanding the graphical effect of f(x+a)
Replies
19
Views
2K
State the domain and range for a given function
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top