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  4. Let f: R → R be such that for all xϵ R (21 + x + 21-x ),f(x) and (3x+3-x) arein A.P., then the minimum value of f(x) is :

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Q. Let $f : R \to R$ be such that for all $x\epsilon R$ $(2^{1 + x} + 2^{1-x} ),f(x)$ and $(3^x+3^{-x})$ arein A.P., then the minimum value of f(x) is :

JEE MainJEE Main 2020Sequences and Series

Solution:

$f \left(x\right)=\frac{2\left(2^{x}+2^{-x}\right)+\left(3^{x}+3x^{-x}\right)}{2}\ge3$
$\left(A.M\ge G.M\right)$