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AP EAMCET · Maths · Functions

If \((f(x))^2=f\left(x^2\right)+f(1)\) holds good, then find \(f(x)\)

  1. A \(x+\frac{1}{x}\)
  2. B \(x-\frac{1}{x}\)
  3. C \(x^2+\frac{1}{x}\)
  4. D \(x-\frac{1}{x^2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x+\frac{1}{x}\)

Step-by-step Solution

Detailed explanation

Given functional relation \((f(x))^2=f\left(x^2\right)+f(\mathrm{l})\) On putting \(f(x)=x+\frac{1}{x}\), the RHS is \(x^2+\frac{1}{x^2}+2=\left(x+\frac{1}{x}\right)^2=(f(x))^2=\text { LHS. }\) Hence, option (a) is correct.