如图，函数$f\left(x\right)$的图象为折线$ACB$，则不等式$f\left(x\right)\ge {\log }_2(x+1)$的解集是（  ）

A．	$\{\overline{)x}-1<x\le 0\}$	B．	$\{\overline{)x}-1\le x\le 1\}$
C．	$\{\overline{)x}-1<x\le 1\}$	D．	$\{\overline{)x}-1<x\le 2\}$