Find \( f(f(f(2))) \)
Question:
If
\[ f(x)=\frac{x+1}{x-1}, \qquad x\ne1 \]
then
\[ f(f(f(2))) \]
is equal to
(a) \(1\)
(b) \(2\)
(c) \(3\)
(d) \(4\)
Solution:
\[ f(2)=\frac{2+1}{2-1}=3 \]
\[ f(f(2))=f(3)=\frac{3+1}{3-1}=2 \]
\[ f(f(f(2)))=f(2)=3 \]
\[ \boxed{\text{Correct Answer: (c)}} \]