Answer the following question based on the information given below.
For a real number $x$, let
f(x)
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= 1/(1 + x),
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if x is non-negative
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= 1+ x,
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if x is negative
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f$^n$(x)
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= f(f$^{n – 1}$(x)), n = 2, 3, ....
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What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$?
- $\frac{1}{3}$
- $3$
- $\frac{1}{18}$
- None of these