Instructions

Directions for the next 2 questions:

For a real number x, let

$$f(x) = 1/(1+x),$$ if $$x$$ is non-negative
$$f(x) = 1+x,$$ if $$x$$ is negative

$$f^n(x) = f(f^{n-1}(x)), n = 2, 3.....$$

Question 126

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

Solution

f(-2) = -1

$$f^2(-2)$$ = f(f(-2)) = f(-1) = 0

$$f^3(-2)$$ = f(f(-2)) = f(0) = 1

So, sum = 0

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