Let f: R → R be such that for all x ∈ 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:

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be such that for all $\displaystyle x \in \mathbf{R}$ $\displaystyle \left(2^{1+x}+2^{1-x}\right), f(x)$ and $\displaystyle \left(3^x+3^{-x}\right)$ are in A.P., then the minimum value of $\displaystyle f(x)$ is :