SOLUTION: If f (x) = x / 1-x find the rule for f ( f (x)) .

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Question 252189: If f (x) = x / 1-x find the rule for f ( f (x)) .
Found 2 solutions by palanisamy, drk:
Answer by palanisamy(496) About Me  (Show Source):
You can put this solution on YOUR website!
Given, f(x) = x/(1-x)
f{f(x)} = [x/(1-x)] / 1-[x/(1-x)]
= [x/(1-x)] / [(1-x-x)/(1-x)]
= x/1-2x

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We want to find f(f(x)). We use order of operations and always start from the inner most parenthesis. We can rewrite f(f(x)) as
f%28x+%2F+%281-x%29%29
which means where ever you see an X, put X/ 1-X. We get
X%2F%281-X%29 / %281-X%2F%281-X%29%29
simplifying the large denominator, we get
X%2F%281-X%29 / %28%281-2X%29%2F%281-X%29%29
multiplying by the reciprocal, we get
X / (1-2X).