TS EAMCET · Maths · Functions
If \(f: R /\{0\} \rightarrow R\) is such that \(2 f(x)+f\left(\frac{1}{x}\right)=4 x\) and \(S=\{x \in R: f(x)=f(-x)\}\), then the number of elements in \(S\) is
- A 0
- B 1
- C 2
- D at least three
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Given, \(2 f(x)+f\left(\frac{1}{x}\right)=4 x\) Replace \(x\) by \(1 / x\), we get, \(2 f(1 / x)+f(x)=\frac{4}{x}\) On multiply by 2 in Eq. (i) and then subtracting Eq. (ii), we get…
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