JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(f: R \rightarrow R\) be such that for all \(\mathrm{x} \in \mathrm{R}\left(2^{1+\mathrm{x}}+2^{1-\mathrm{x}}\right), f(\mathrm{x})\) and \(\left(3 ^\mathrm{x}+3^{-\mathrm{x}}\right)\) are in \(A.P.\), then the minimum value of \(f(x)\) is
- A \(0\)
- B \(3\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{2\left(2^{x}+2^{-x}\right)+\left(3^{x}+3^{-x}\right)}{2} \geq 3\) \((A . M \geq G . M)\)
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