重难点 抽象函数及其应用（学生版）

A.(-2,0(∪(0,2(B.(-1,3(C.(-3,0(∪(0,1(D.(-1,0(∪(0,3(A.函数y=2x+、x-1的值域为[2,+∞(B.函数f(x(=tanx的值域为RC.函数f(x(=ex-1与g(x是同一个函数D.若函数f(x-1(的定义域为[1,4[，则函数f(2x(的定义域为[0,2[有f(f(x(-log2x(=3，则f(22025)-2的值是()f(x(=x(2-x(，则f(9(=；x∈(-4,-2[时，f(x(=．5.(24-25高二下·广东云浮·期末)已知函数f(x(的定义域为R，满足f(x+y(>f(x(.f(y(，且f(1(=1122A.f(10(>104B.f(20(>106C.f(10(<104D.f(20(<106f(y(+1=f(x+y(，则()A.f(-2(=-3B.f(2025(=2024C.f(x(有最大值D.f(x(+1是奇函数f(x(f(y(，且f(1(=2，则++…+=()7.(23-24高一上·广东江门·期末)已知函数f(x(的定义域为R，对于任意实数x，y满足ff(x(f(y(，且f(1(=2，则++…+=()f(1(f(3(f(2023(8.(24-25高一上·广东佛山·期末)已知定义在R上的函数f(x(满足f(x+y，且当x>0时，0<f(x(<1，则f(x(是()A.奇函数，在(0,+∞(上单调递增B.奇函数，在(0,+∞(上单调递减9.【多选】(23-24高三上·广东汕头·期末)已知定义在(0,+∞(上的函数f(x(满足：∀x,y∈(0,+∞(，f(x(+f(y(=f(xy(，且当0<x<1时，f(x(<0，若f(2(=1，则()A.f(1(=0B.f(x(在(0,+∞(上单调递减C.|f(x(|=|fD.f(2(+f(22(+…+f(220(=5510.(23-24高一上·广东珠海·期末)已知定义在R上的函数f(x(满足f(xy(=f(x(f(y(-f(x(-f(y(+f(0(<f(1(，且f(x(>0.(1)求f(-1(的值；11.(23-24高一上·广东梅州·期末)已知f(x(是定义在R上且不恒为零的函数，对于任意实数a,b满足f(ab(=af(b(+bf(a(，若f(3(=2，则f(-1(+f(-=()A.B.C.D.-3312.(24-25高一上·广东深圳·期末)设函数f(x(是定义在R上的周期为4的偶函数，当x∈[-2,0[时，f(x(=x+1，则f(5(=()A.-2B.0C.2D.613.(24-25高二下·广东深圳·期末)定义在R上的奇函数f(x(满足f(2-x(=f(x(，且f(11(+f(10(=-1，则f(1(=．14.(22-23高三上·广东·期末)已知函数f(x(，∀x，y∈R，有f(x+y(=f(x(.f(a-y(+f(y(.f(a-x(，A.4a是f(x(的一个周期B.f(x(是奇函数C.f(x(是偶函数D.f(a(=1<时，f(x(=(x-2，则f=．16.(24-25高三上·广东湛江·期末)已知函数f(x(满足f(x-2(+f(-x(=0，且f(x+1(是奇函数，若f(2(=3，则f(9(+f(10(=()A.-6B.-3C.3D.6(1-x)f(x-1)-f(x-2),17.(24-25高二上·广东广州(1-x)f(x-1)-f(x-2),f(2024)的值为()A.-1B.0C.1D.2x≤0x>018.(22-23高二上·广东深圳·期末)已知定义域为R的函数f(x(满足f(3x+1(是奇函数，f(2x-1(是偶A.f(x(的图象关于直线x=-1对称B.f(x(的图象关于点(1,0)对称C.f(-3(=1D.f(x(的一个周期为8(-|x+2|,x<0(-|x+2|,x<020.(24-25高一下·广东广州·期末)已知函数f(x(,g(x(的定义域均为R，且f(x)+g(1-x)=3，g(x(+44A.f(-x(=-f(x(B.g(-x(=-g(x(C.=6066DA.4是f(x)的一个周期B.f(x)的图象关于直线x=2对称CD.方程f(x)=ln|x|恰有8不同的实数根22.(24-25高一上·广东汕尾·期末)若函数f(x)=(x2-2x)(x2+mx+n)的图象关于直线x=-1对称，则m+n=，f(x)的最小值为.A.充要条件B.充分不必要条件C.必要不充分条件D.既不充分也不必要条件A.(-∞,1)B.(-1,1)C.(-3,1)D.(-∞,1]不等式f(x-2(<f(3(的解集为()A.(-1,5(B.(-∞,-1(∪(2,5(C.(-∞,-1(∪(5,+∞(D.(-1,2(∪(5,+∞(26.(24-25高一上·广东深圳·期末)已知函数f(x)是定义域为R的奇函数，且f(x)在[0,+∞)上单调递减．若f(3+m)+f(3m-7)>0，则m的取值范围为()A.(-∞,0)B.(0,+∞)C.(-∞,1)D.(1,+∞)27.(22-23高一上·广东深圳·期末)若f(x(是偶函数且在[0,+∞(上单调递增，又f(-2(=1，则不等式f(x(>1的解集为()A.{x|-2<x<2{B.{x|x<-2或x>2}C.{x|x<-2或0<x<2}D.{x|x>2或-2<x<0}5528.(22-23高一上·广东肇庆·期末)已知函数f(x(的定义域是R，函数f(x+1(的图象的对称中心是f(x(-x>0的解集为()A.(-∞,-1(∪(1,+∞(B.(-1,1(C.(-∞,-1(∪(0,1(D.(-1,0(∪(1,+∞(29.(25-26高一上·广东·期末)设偶函数f(x)的定义域为R，当x∈[0,+∞(时，f(x)是-7)，f(π(，f(-3)的大小关系是()A.f(π(>f(-3(>f(-7(B.f(π(>f(-7(>f(-3(C.f(π(<f(-3(<f(-7(D.f(π(<f(-7(<f(-3(30.(22-23高二上·广东·期末)已知定义在R上的函数f(x(满足：f(-x(+f(x(=0，f(2-x(=f(x(，且A.f(-5.3(<f(5.5(<f(2(B.f(-5.3(<f(2(<f(