If f(x) = `(x + 1)/(x-1)` , then the value of f{f(3)} is :

Options

A. 3
B. 2
C. 6
D. None of these

Answer

To solve the problem, we need to find the value of \( f(f(3)) \) given the function \( f(x) = \frac{x + 1}{x - 1} \).

### Step-by-Step Solution:

1. **Find \( f(3) \)**:
\[ f(3) = \frac{3 + 1}{3 - 1} \]
Simplifying this:
\[ f(3) = \frac{4}{2} = 2 \]

2. **Now find \( f(f(3)) \)**, which is \( f(2) \):
\[ f(2) = \frac{2 + 1}{2 - 1} \]
Simplifying this:
\[ f(2) = \frac{3}{1} = 3 \]

3. **Final Result**:
Therefore, \( f(f(3)) = f(2) = 3 \).

### Conclusion:
The value of \( f(f(3)) \) is \( 3 \).

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