對(duì)數(shù)函數(shù)習(xí)題與答案

1、習(xí)題課習(xí)題課——對(duì)數(shù)函數(shù)及其性質(zhì)的應(yīng)用對(duì)數(shù)函數(shù)及其性質(zhì)的應(yīng)用一、一、A組1.已知函數(shù)y=loga(xc)(ac為常數(shù)且a0a≠1)的圖象如圖所示則下列結(jié)論成立的是()A.a1c1B.a101D.0bcB.acbC.cbaD.cab解析:∵0lo=1∴cab.故選D.2131312131212答案:D3.函數(shù)f(x)=的定義域?yàn)?)32(3)A.(35]B.[35]C.[53)D.[53]解析:要使函數(shù)有意義則3log2(3x)≥0即lo

2、g2(3x)≤3∴00可得x2或xloga(42x).當(dāng)a1時(shí)可得x142x解得x1.由(1)知11時(shí)x的取值范圍是(12)當(dāng)0a1時(shí)x的取值范圍是(11).9.導(dǎo)學(xué)號(hào)29900105若3≤lox≤求f(x)=的最值.1212(22)(24)解:f(x)=(22)(24)=(log2x1)(log2x2)=(log2x)23log2x2.令log2x=t∵3≤lox≤1212∴3≤log2x≤12∴≤log2x≤3.∴t∈.12[123

3、]∴f(x)=g(t)=t23t2=.(32)2?14∴當(dāng)t=時(shí)g(t)取最小值3214此時(shí)log2x=x=2322當(dāng)t=3時(shí)g(t)取最大值2此時(shí)log2x=3x=8.綜上當(dāng)x=2時(shí)f(x)取最小值214當(dāng)x=8時(shí)f(x)取最大值2.二、二、B組1.(2016江西南昌二中高一期中)函數(shù)y=xln|x|的大致圖象是()解析:函數(shù)f(x)=xln|x|的定義域(∞0)∪(0∞)關(guān)于原點(diǎn)對(duì)稱且f(x)=xln|x|=xln|x|=f(x)所