1.
Let f(x)=x+1x1f(x) = \frac{x+1}{x-1} for all x1x \ne 1. Let f1(x)=f(x)f^1(x) = f(x), f2(x)=f(f(x))f^2(x) = f(f(x)) and generally fn(x)=f(fn1(x))f^n(x) = f(f^{n-1}(x)) for n>1n > 1. Let P=f1(2)f2(3)f3(4)f4(5)P = f^1(2) \cdot f^2(3) \cdot f^3(4) \cdot f^4(5). Which of the following is a multiple of PP?