Question

If x ≠ 1 and $f\left(x\right)=\frac{x+1}{x-1}$is a real function, then f(f(f(2))) is
(a) 1
(b) 2
(c) 3
(d) 4

Answer 1

(c) 3
$f\left(x\right)=\frac{x+1}{x-1}$
$$\begin{gathered} f\left(f\right(f\left(2\right)\left)\right) \\ =f\left(f\left(\frac{2+1}{2-1}\right)\right) \\ =f\left(f\left(3\right)\right) \\ =f\left(\frac{3+1}{3-1}\right) \\ =f\left(2\right)=3 \end{gathered}$$