2^(x-0.5)+((корень из 2)/2)>1+2^-x
t=2^x
t>0
1+1/t" alt="t/ \sqrt{2}+1/ \sqrt{2} >1+1/t" align="absmiddle" class="latex-formula">
\sqrt{2} (t+1)" alt=" t(t+1)> \sqrt{2} (t+1)" align="absmiddle" class="latex-formula">
сокращаем на T+1 так как больше 0
\sqrt{2} " alt="t> \sqrt{2} " align="absmiddle" class="latex-formula">
2^{1/2}" alt="2^x>2^{1/2}" align="absmiddle" class="latex-formula">
x>1/2