Question

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 :

• A. 0
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (C)

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