Question 9

Mathematics Function and Relation Medium

The value of \(f(1)\) for \(f(\frac{1-x}{1+x}) = x+2\) is:

(A) 1
(B) 2
(C) 3
(D) 4
✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

We are given the functional equation: \[ f\left(\frac{1 - x}{1 + x}\right) = x + 2. \] To find the value of \( f(1) \), we substitute \( x = 0 \) into the equation: \[ f\left(\frac{1 - 0}{1 + 0}\right) = 0 + 2. \] Simplifying: \[ f(1) = 2. \]

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