If x ≠ 1 and f(x)=

Question:

If $x \neq 1$ and $f(x)=\frac{x+1}{x-1}$ is a real function, then $f(f(f(2)))$ is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

(c) 3

$f(x)=\frac{x+1}{x-1}$

$f(f(f(2)))$

$=f\left(f\left(\frac{2+1}{2-1}\right)\right)$

$=f(f(3))$

$=f\left(\frac{3+1}{3-1}\right)$

$=f(2)=3$

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