Q117 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

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

  • Correct answer
    A
    \(x+\frac{1}{x}\)
  • B
    \(x-\frac{1}{x}\)
  • C
    \(x^2+\frac{1}{x}\)
  • D
    \(x-\frac{1}{x^2}\)

Solution

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.

Hence, the correct answer is option: 'A'.

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