Solution of ${2^x} + {2^{\left| x \right|}} \ge 2\sqrt 2 $ is

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

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

JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

1 of 1

Analyzing +4 | -1

Solution of

{2^x} + {2^{\left| x \right|}} \ge 2\sqrt 2

View answer and explanation

Correct option: D

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

Option D (

(- \infty, {\log_2}(\sqrt{2} - 1)) \cup [\frac{1}{2}, \infty)

) is correct because it represents the complete solution set obtained by considering both positive and negative values of x.