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If f(x) =x+1x−1\frac{x+1}{x-1}x−1x+1​​, find the value of f(f(2))).
Question

If f(x) =x+1x1\frac{x+1}{x-1}​, find the value of f(f(2))).

A.

2

B.

1

C.

-1

D.

3

Correct option is A

Given:
Function f(x) =x+1x1 \frac{x+1}{x-1}​​
We need to find the value of f(f(2)) .
Formula Used:
First, calculate f(2) using the function f(x) =x+1x1 \frac{x+1}{x-1}​ , then substitute this result back into the function to find f(f(2)) .
Solution:
 Calculate f(2) :
f(2)=2+121=31=3f(2) = \frac{2+1}{2-1} = \frac{3}{1} = 3​​
 Calculate f(f(2)) = f(3) :
f(3)=3+131=42=2f(3) = \frac{3+1}{3-1} = \frac{4}{2} = 2​​
Therefore, the value of f(f(2)) = 2 .

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