Question

given f(x)=(1/(1-x)), find f(f(x)) and simplify. a medal to who can get the answer and explain how they did it.

Answer 1

Okay so\[
f(x)=\frac{1}{1-x}
\]

Answer 2

Then \[
f(f(x)) = \frac{1}{1-f(x)}
\]Do you follow so far?

Answer 3

yes I have gotten (1/(1-(1/(1-x)))) but im not sure if I can simplify it.

Answer 4

\(\bf f(x) = \cfrac{ 1 }{ 1-x }\\
f(\quad f(x)\quad ) = \cfrac{ 1 }{ 1-\left( \frac{ 1 }{ 1-x } \right) }\implies \cfrac{ 1 }{ \frac{ 1 }{ 1 }- \frac{ 1 }{ 1-x } }\)

what would you get for the 2 fractions subtraction in the denominator of \(\bf \cfrac{ 1 }{ 1 }- \cfrac{ 1 }{ 1-x } \ ?\)

Answer 5

So it would be something like:
(x-1/x-1) - (1/x-1)
which becomes
(1-x-1)/(x-1)
which is
-x/(x-1) right?

Answer 6

well.... what would be the LCD from "1" and "1-x"?

Answer 7

Actually \[
\frac{1-x}{1-x}-\frac{1}{1-x} = \frac{-x}{1-x}
\]

Answer 8

\(\bf f(x) = \cfrac{ 1 }{ 1-x }\\
f(\quad f(x)\quad ) = \cfrac{ 1 }{ 1-\left( \frac{ 1 }{ 1-x } \right) }\implies \cfrac{ 1 }{ \frac{ 1 }{ 1 }- \frac{ 1 }{ 1-x } }\\ \quad \\ \quad \\
\cfrac{ 1 }{ \frac{ (1-x)-1 }{ 1-x } } \implies \cfrac{ 1 }{ \frac{ 1-x-1 }{ 1-x } } \implies \cfrac{ 1 }{ \frac{-x }{ 1-x } }
\implies \cfrac{ 1 }{ 1 } \times \cfrac{ 1-x }{-x }\)

Answer 9

I think the most simplified from is: \[
\frac {x-1}{x}=1-\frac 1x
\]

Answer 10

no i think it is \[(1-x)/-x \]