# Swapping the values

Calculus Level 3

$\large f(x)=\left (2^{x}+\frac{1}{2^{x}}\right)\left (x^{2}+\frac{1}{x^{2}} \right)$

If $$x \in \mathbb{R}$$, then what is the minimum value of $$\lceil f(x) \rceil$$?

Notation: $$\lceil \cdot \rceil$$ denotes the ceiling function.

×