TS EAMCET · Maths · Functions
If \(f: \mathrm{R}-\{0\} \rightarrow \mathrm{R}\) is defined by \(3 f(x)+4 f\left(\frac{1}{x}\right)=\frac{2-x}{x}\) then \(f(3)=\)
- A \(6\)
- B \(12\)
- C \(9\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
Substitute \(x=3\): \(3 f(3)+4 f\\left(\\frac{1}{3}\\right)=-\\frac{1}{3}\) (1) Substitute \(x=\\frac{1}{3}\): \(3 f\\left(\\frac{1}{3}\\right)+4 f(3)=\\frac{2-\\frac{1}{3}}{\\frac{1}{3}} = 5\) (2) From (1) \(\times 3\): \(9 f(3)+12 f\\left(\\frac{1}{3}\\right)=-1\) From (2)…
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