2023学年高考数学大二轮复习大题专项练七选做题文2.docx

大题专项练(七)选做题A组基础通关1.(2023辽宁沈阳东北育才学校八模)已知函数f(x)=|x-1|+|x+1|.(1)求f(x)≥3的解集;(2)记函数f(x)的最小值为M,若a>0,b>0,且a+2b=M,求1a+2b的最小值.解(1)由f(x)≥3,得{x≤-1,-\(x-1\)-\(x+1\)≥3或{-11,\(x-1\)+\(x+1\)≥3,即{x≤-1,x≤-32或{-11,x≥32.解得x≤-32或x≥32,∴不等式f(x)≥3的解集为-∞,-32∪32,+∞.(2) f(x)=|x-1|+|x+1|≥|(x-1)-(x+1)|=2,∴f(x)的最小值M=2,∴a+2b=2, a>0,b>0,∴1a+2b=(1a+2b)·a+2b2=125+2ba+2ab≥125+2❑√2ba·2ab=92,当且仅当2ba=2ab即a=b=23时等号成立,1∴1a+2b的最小值为92.2.(2023江西赣州5月适应性考试)已知函数f(x)=|x+1|+2|x-1|.(1)求不等式f(x)≤4的解集;(2)若函数y=f(x)图象的最低点为...