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Answer the following question based on the information given below.
For a real number $x$, let

f(x)

= 1/(1 + x),

if x is non-negative

 

= 1+ x,

if x is negative

f$^n$(x)

= f(f$^{n – 1}$(x)), n = 2, 3, ....

 

What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$?

  1. $\frac{1}{3}$
  2. $3$
  3. $\frac{1}{18}$
  4. None of these
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