I know this is really simple, but can someone help?
f(x) = x+1/x-1
find (f o f)(x)
Thanks!!
Hello, rtwilton
$\displaystyle f(x) \:= \:\frac{x+1}{x-1}$
Find: .$\displaystyle (f\circ f)(x)$
$\displaystyle (f\circ f)(x) \;=\;f(f(x)) \;=\;f\left(\frac{x+1}{x-1}\right) \;=\;\frac{\dfrac{x+1}{x-1} + 1}{\dfrac{x+1}{x-1} - 1}$
Multiply by $\displaystyle \frac{x-1}{x-1}\!:\quad\frac{(x-1)\left(\dfrac{x+1}{x-1} + 1\right)} {(x-1)\left(\dfrac{x+1}{x-1} - 1\right)} \;=\;\frac{(x+1) + (x-1)}{(x+1) - (x-1)} \;=\;\frac{2x}{2} \;=\;\boxed{ x}$
Note: This means that $\displaystyle f(x)$ is its own inverse!