專(zhuān)題復(fù)習(xí)之--函數(shù)零點(diǎn)問(wèn)題

1、專(zhuān)題復(fù)習(xí)之-函數(shù)零點(diǎn)問(wèn)題(一)零點(diǎn)所在區(qū)間問(wèn)題(存在性，根的分布)1 .函數(shù)f (x) = lg x + x -3的零點(diǎn)所在區(qū)間為()A. (0, 1) B. (1 , 2) C. (2, 3) D. (3, +叫變式：函數(shù)f(x)=ax + xb的零點(diǎn)x0w(n,n+1)(nwZ),其中常數(shù)a,b滿(mǎn)足 2a =3,3b =2 ,則 n =()A. 0B.1C. -2D. -12 .已知a是實(shí)數(shù)，函數(shù) f (x) =2ax2+2x3 a,如果函數(shù)y = f (x)在區(qū)間11上有零 點(diǎn)，則a的取值范圍是.(二)零點(diǎn)個(gè)數(shù)問(wèn)題(重點(diǎn)，常用數(shù)形結(jié)合)3 .函數(shù)f (x) = Jx + 4 + x -

2、4的零點(diǎn)有 個(gè).4 .討論函數(shù)f (x) = x2 -1 a的零點(diǎn)個(gè)數(shù)5 .若存在區(qū)間a,b,使函數(shù)f (x) = k+Jx + 2 (x亡fa,b】)的值域是a,b,則實(shí)數(shù)k的范圍是.6 .已知偶函數(shù)f (x)滿(mǎn)足f (2x) = f (x),且當(dāng)0Wx<1時(shí)，f (x) = x ,則f (x) = lg x的零精品資料點(diǎn)個(gè)數(shù)是223420122013 、一xxx x x7.(選作思考)函數(shù) f (x) = 1 +x-+ 一+-cos2x 在區(qū)間-3,、234 T T 2012 2013 y3上的零點(diǎn)的個(gè)數(shù)為 (三)復(fù)合函數(shù)與分段函數(shù)零點(diǎn)問(wèn)題(由里及外，畫(huà)圖分析)8.已知函數(shù)f(x)=

3、3xJog3(-x)(X °),函數(shù) g(x) = f2 (x) + f (x) +t(t w R).關(guān)于 g (x)的 (x < 0)零點(diǎn)，下列判斷不正確 的是() 41, 一，人.右1 = 一,g(x)有一個(gè)零點(diǎn) 4C.若t = -2,g(x)有三個(gè)零點(diǎn)心1B.若-2<t <-,g(x)有兩個(gè)零點(diǎn)4D.若t<-2, g(x)有四個(gè)零點(diǎn)、.5|xJ1 -1.x - 0.、變式一：設(shè)定義域?yàn)镽的函數(shù)f(x)=,，若關(guān)于x的方程x2 4x 4,x : 022f (x) (2m+1)f (x)+m =0有5個(gè)不同的實(shí)數(shù)解，則 m=()A. 2 B. 6 C. 2

4、或 6D. 4 或 6,lg x設(shè)定義域?yàn)镽的函數(shù)f (x)=/廣-x2 -2x(x>0)(x 三 0)則關(guān)于x的函數(shù)2 , y=2f (x)-3f(x)+1的零點(diǎn)的個(gè)數(shù)為； x_,ex(x _0) 一，口，x的方程:已知函數(shù)f (x) = «(),則實(shí)數(shù)t W 2是關(guān)于lg(-x) (x ：:0)-2 ,f (x) f (x) t =0 .有三個(gè)不同實(shí)數(shù)根的(A.充分不必要條件B.必要不充分條件C.充分必要條件D.既不充分也不必要條件9.已知函數(shù)f(x)=lx+-(x = 0)2.則關(guān)于x的方程 f (x)+bf(x1c= 01 5個(gè)(x=0)不同的實(shí)數(shù)解的充要條件是(A.

5、b<-2 且 c>0 B. b>-2 且 c<0 C. b<-2 且 c=0 D. b 22且c=01 八 x+ ,x>0 10.已知函數(shù)f(x)=«x3,x < 0則函數(shù)F(x)2=f (2x +x) -a(a > 2)的零點(diǎn)個(gè)數(shù)不目能為() A. 3B. 4C. 5D. 6ax + 1, x <011 .已知函數(shù)f(x)=1，則下列關(guān)于函數(shù) y=f(f(x)+1的零點(diǎn)個(gè)數(shù)的判斷正確的Jog2 x, x >0是()A.當(dāng)a>0時(shí)，有4個(gè)零點(diǎn)；當(dāng)a<0時(shí)，有1個(gè)零點(diǎn)B.當(dāng)a>0時(shí)，有3個(gè)零點(diǎn)；當(dāng)a<0時(shí)，有2個(gè)零點(diǎn)C.無(wú)論a為何值，均有2個(gè)零點(diǎn)D.無(wú)論a為何值，均有4個(gè)零點(diǎn)(四)零點(diǎn)值的和，積或其它運(yùn)算結(jié)果的值(范圍)的問(wèn)題1 0若a, b,c為互不相等實(shí)數(shù)且| l 整 | < x0_12 .已知函數(shù)f (x)=<1x 6 x 102f (a) = f (b) = f (c),則abc的取值范圍是()A. (1,10)B.(5,6)C.(10,12)D.(20,24)1, x >0變式：定義符號(hào)函數(shù)為 sgn(x) = « 0, x = 0 ,設(shè)函數(shù)f (x) = 1g x sgn(lg x)+k(k >0)的零 1,x < 0點(diǎn)為a,b(