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

[Jpyhsics]

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.

 

[PeroK]

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 $f(f(-1)$?

 

[Jpyhsics]

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!

 

[Ray Vickson]

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 $D = (-1/2,\infty).$