函數(shù)定義域與函數(shù)值

1、、函數(shù)的定義域1、一般函數(shù)的定義域f (x)為整式型函數(shù)時,定義域為R ；f (x)為分式型函數(shù)時,定義域為使分母不為0的實數(shù)的集合；f (x)為二次根式(偶次根式)型函數(shù)時,定義域為使被開方數(shù)非負的實數(shù)的集合；(4)若f (x)是由幾個部分的數(shù)學式子構成的，則函數(shù)的定義域是使各部分都有意義的實數(shù)的集合，即交集；f (x) = x0的定義域是x E R I x豐0.例1、求下列函數(shù)的定義域.(1) y = 2x + 3(2) y = x(3) y = vx-1 -、,：1 x2 x 2 - 3 x - 2y =3(5) y = x2 -3 + %：5-x2- 11 - x抽象函數(shù):沒有給出具體

2、解析式的函數(shù).2、抽象函數(shù)的定義域函數(shù)f (x)的定義域是指x的取值范圍；函數(shù)f (g(x)的定義域還是指x的取值范圍,而不是g(x)的范圍；已知f (x)的定義域為A，求f (g (x)的定義域,其實質(zhì)是已知g (x)的取值范圍為A,求x的 取值范圍；(4)已知f (g(x)的定義域為B ,求f (x)的定義域,其實質(zhì)是已知f (g(x)中x的取值范圍為B , 求g(x)的范圍(值域)，此范圍就是f (x)的定義域；(5)已知f (g(x)的定義域，求f (h(x)的定義域，先由x的取值范圍求出g(x)的取值范圍，即 f (x)中x的取值范圍,亦即h(x)的取值范圍,再根據(jù)h(x)的取值范圍

3、求出x的取值范圍.注：f (t), f (g(x), f (h(x)三個函數(shù)中的t, g(x),h(x)在對應關系f下的范圍相同.例2、求下列抽象函數(shù)的定義域.(1)已知函數(shù)f (x)的定義域是-1,4,求函數(shù)f (2x +1)的定義域.(2)已知函數(shù)f (2x-1)的定義域是-3,3,求函數(shù)f (x)的定義域.(3)已知函數(shù)f (2x-1)的定義域是0,1)，求函數(shù)f (1 -3x)的定義域.11,例3、已知函數(shù)f (x)的定義域是0,2,求g (x) = f (x + -) + f (x -)的定義域. 22課后練習一1、已知函數(shù)f (x)的定義域為(-1,0)，則函數(shù)f (2X +1)的

4、定義域為2、已知函數(shù)f(x)7-x2 + 2x + 3的,則函數(shù)f (3x-2)的定義域為3、已知函數(shù)f (x2-1)的定義域為0,3,則函數(shù)f (x)的定義域為14、已知函數(shù)f (x +1)的定義域為- ,2,則函數(shù)f (x-1)的定義域為 25、設函數(shù)f (x) = G，則f (7、若函數(shù)y = f (x)的定義域是0,2,7、若函數(shù)y = f (x)的定義域是0,2,則函數(shù)g(x)= 必)的定義域為 -16、若函數(shù)y = f (x)的定義域為-2,4,則函數(shù)g(x) = f (x) + f (-x)的定義域為二、函數(shù)的求值問題函數(shù)值的求法已知函數(shù)解析式求函數(shù)值：當自變量為確定的數(shù)值時，直

5、接將自變量的值代入解析式即 可求出相應的函數(shù)值;當自變量為包含字母的代數(shù)式時，將代數(shù)式整體代入求解.求類似f (g(x)的值時，要注意f,g作用對象,按“由內(nèi)到外”的順序取值.對于抽象函數(shù)的求值問題,一般采用賦值法.1例 4、已知 f (x)=，g(x) = x2 + 2.1 + x求f (2), g的值；(2)求f (g(2)的值；求 f (g(x), g(f (x)的解析式；(4)若 1= 4，求 x .f (g (x)- 2x, x G (-8,-1) 11.例 5、已知函數(shù) f (x) = J2,x g -1,1分別求 f (-2), f (Rf (4.5), f (f 0)的值.2x

6、, x G (1,+8)例6、已知函數(shù)f (x)對任意實數(shù)a,b,都有f (ab) = f (a) + f (b)成立.求f (0), f (1)的值；若 f (2) = p, f (3) = q (p, q 為常數(shù))，求 f (36)的值.課后練習二8、已知 f(x) = - (x g R 且 x w1), g(x) = x2 -1(x e R). 1 + x求f (2), g(3)的值；求f (g(3)的值及f (g(x).5 x9、若 f (x )=，且 f (a ) = 2，貝U a =.x 2 +110、設常數(shù) a e R，函數(shù) f (x) =1 x -11 +1 x 2 - a I

7、,若 f (2) = 1,則 f =.11、若函數(shù) f (x) = 1 -2x, g(f (x) = 1x2(x w 0)，則 g(i) =. x 2212、若函數(shù) f (x) = ax2-、2, a 為正實數(shù)，且 f (f (&) = -、2，則 a =.13、已知函數(shù)y = f (x)的定義域為(0,+8),且對定義域內(nèi)的任一 x, y都有f (xy) = f (x) + f (y), 若 f = 1，則 f(v2)=.14、已知 f (0) = 1, f (n) = nf (n -1),n e N*，則 f (3) =.15、已知 a, b e N *, f (a + b ) = f (a) f (b), f (1) = 2，則 f2 + f3) +. + f(2013) f (1)f (2)f (2012)f (2014)_ .f(2013)x 216、已知 f (x) =, x e R .1 + X 2 TOC o 1-5 h z ，、,、1求f (a) + f的值； a111 .計算 f (1) + f (2) + f (-) + f (3) + f (-) + f (4) + f (-