GMAT Problem Solving- Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ?

Question: Given f(x) = x/(x + 1), for what value k does f(f(k)) = 2/3 ?

1. –2
2. 5/3
3. 1
4. 2
5. 8

“Given f(x) = x/(x + 1), for what value k does f(f(k)) = 2/3 ?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

This question can be solved by only one approach.

Explanation:
Given to us in the question a function
f(x) = x/(x+1)
It has asked to find out the value of k for which f(f(k)) = ⅔
This is a question of relation and functions.
Given : f(x) = x/(x+1)
f(k) = k/(k+1)
f(f(k)) = f(k) / (f(k)+1) replacing the value of k by f(k)
putting the value of f(k) we get,
f(f(k)) = k/(k+1) / (k/(k+1))+1)
f(f(k)) = k/(k+1) * k+1/(2k+1)
Given that f(f(k)) = ⅔
k/(k+1) * k+1/(2k+1) = ⅔
k/(2k+1) = ⅔
3k = (2k+1) *2
3k = 4k + 2
K = -2
The value of k is -2 so that to make the value of f(f(k)) = ⅔

Correct Answer: C

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