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CAT 2000 | Question: 88

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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, ....

  

$r$ is an integer $\geq 2.$ Then what is the value of $f^{r-1}(-r) + f^r(-r)+f^{r+1}(-r)$?

  1. $-1$
  2. $0$
  3. $1$
  4. None of these
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