Let be a function defined by

MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions

Problem

Let

f: R \to R

be a function defined by

f(x+1) = \frac{f(x)-5}{f(x)-3}, \forall x \in R

. Then, which of the following statements is/are true? (1)

f(2008) = f(2004)

(2)

f(2006) = f(2010)

(3)

f(2006) = f(2002)

(4)

f(2006) = f(2018)