COMEDK · Maths · 24. Functions
If \(f(x)+2 f(1-x)=x \forall x \in R\), then \(f(x)\) is equal to
- A \(2-3 x\)
- B \(\frac{1}{2}(2-3 x)\)
- C \(\frac{1}{3}(2-3 x)\)
- D \(\frac{1}{3}(2 x-3)\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{3}(2-3 x)\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)+2 f(1-x)=x\)...(i) Now, replace \(x\) by \(1-x\) \(\begin{array}{r} \therefore f(1-x)+2 f(1-(1-x))=1-x \\ f(1-x)+2 f(x)=1-x ...(ii)\mid \end{array}\) Multiply by 2 to the Eq. (ii) and subtract from Eq. (i),…
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