AP EAMCET · Maths · Functions
If \((f(x))^2=f\left(x^2\right)+f(1)\) holds good, then find \(f(x)\)
- A \(x+\frac{1}{x}\)
- B \(x-\frac{1}{x}\)
- C \(x^2+\frac{1}{x}\)
- D \(x-\frac{1}{x^2}\)
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.
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