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TS EAMCET · Maths · Functions

\(f\) is real valued function satisfying the relation \(f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}\). If \(f\left(x+\frac{1}{x}\right)=1\) then \(x=\)

  1. A \(\pm 2\)
  2. B \(\pm 1\)
  3. C \(\pm 3\)
  4. D \(\pm 6\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\pm 1\)

Step-by-step Solution

Detailed explanation

Given that \(f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}\) \(f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}+2 \cdot 3 x \cdot \frac{1}{2 x}-3\) \(\Rightarrow f\left(3 x+\frac{1}{2 x}\right)=\left(3 x+\frac{1}{2 x}\right)^2-3\) \(\therefore f(x)=x^2-3\)…