Question

Помогите пожалуйста разобраться

Answer 1

$\frac{4^{x}+2x-4}{x-1}\leq 2\; ,\; \; \frac{4^{x}+2x-4}{x-1}-2\leq 0\; ,\; \; \frac{4^{x}+2x-4-2x+2}{x-1}\leq 0\\\\ \frac{4^{x}-2}{x-1}\leq 0\\\\a)\; \; \left \{ {{4^{x}-2\leq 0} \atop {x-1>0}} \right. \; \left \{ {{2^{2x}\leq 2^1} \atop {x>1}} \right. \; \left \{ {{2x\leq 1} \atop {x>1}} \right. \; \left \{ {{x\leq \frac{1}{2}} \atop {x>1}} \right. \; \Rightarrow \; x\in \varnothing \\\\b)\; \; \left \{ {{4^{x}-2\geq 0} \atop {x-1<0}} \right. \; \left \{ {{2^{2x}\geq 2} \atop {x<1}} \right. \; \left \{ {{2x\geq 1} \atop {x<1}} \right. \; \left \{ {{x\geq \frac{1}{2}} \atop {x<1}} \right. \; \Rightarrow \; \frac{1}{2}\leq x<1\\\\Otvet:\; \; x\in [\, \frac{1}{2};1\, )\; .$