JEE Main 2020 (Online) 8th January Morning ShiftQuestion 1
Let $f:\mathbf{R}\to\mathbf{R}$ be such that for all $x\in\mathbf{R}$, $(2^{1+x}+2^{1-x})$, $f(x)$ and $(3^x+3^{-x})$ are in A.P., then the minimum value of $f(x)$ is :
Sets, Relations and Function
Solution
$2f(x)=2^{1+x}+2^{1-x}+3^x+3^{-x}=2(2^x+2^{-x})+(3^x+3^{-x})\ge 4+2=6$ by AM-GM, equality at $x=0$. So $f_{\min}=3$. Option (C).