Solution of \(2^x+2^{|x|} \geq 2 \sqrt{2}\) is :

\(\left(-\infty, \log _2(\sqrt{2}+1)\right)\)

\((0, \infty)\)

\(\left(\frac{1}{2}, \log _2(\sqrt{2}-1)\right)\)

\(\left(-\infty, \log _2(\sqrt{2}-1)\right] \cup\left[\frac{1}{2}, \infty\right)\)