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AP EAMCET · Maths · Quadratic Equation

\(f(x)\) is an \(n^{\text {th }}\) degree polynomial satisfying \(f(x)=\frac{1}{2}\left|\begin{array}{cc}f(x) & f\left(\frac{1}{x}\right)-f(x) \\ 1 & f\left(\frac{1}{x}\right)\end{array}\right|\). If \(f(2)=33\), then the value of \(f(3)\) is

  1. A \(126\)
  2. B \(214\)
  3. C \(244\)
  4. D \(-124\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(244\)

Step-by-step Solution

Detailed explanation

\(f(x)=\frac{1}{2}\left(f(x)f\left(\frac{1}{x}\right) - \left(f\left(\frac{1}{x}\right)-f(x)\right)\right)\) \(2f(x) = f(x)f\left(\frac{1}{x}\right) - f\left(\frac{1}{x}\right) + f(x)\) \(f(x) = f\left(\frac{1}{x}\right)(f(x)-1)\) Let \(P(x) = f(x)-1\). Then \(f(x) = P(x)+1\).…