Find \( f(f(1/x)) \)
Question:
If
\[ f(x)=1-\frac1x, \]
then write the value of
\[ f\left(f\left(\frac1x\right)\right). \]
Solution:
First,
\[ f\left(\frac1x\right) = 1-\frac{1}{1/x} \]
\[ =1-x \]
Now,
\[ f(f(1/x)) = f(1-x) \]
\[ =1-\frac1{1-x} \]
\[ =\frac{1-x-1}{1-x} \]
\[ =\frac{x}{x-1} \]
Therefore,
\[ \boxed{f(f(1/x))=\frac{x}{x-1}} \]