2025新高考重难点之构造函数 学生版.docx

重难点之构造函数

1.对于不等式f/(x(k(k≠0(，构造函数g(x(=f(x(-kx+b

2.对于不等式xf/(x(+f(x(0，构造函数g(x(=xf(x(

3.对于不等式xf/(x(-f(x(0，构造函数g(x(=(x≠0(

4.对于不等式xf/(x(+nf(x(0，构造函数g(x(=xnf(x)

5.对于不等式xf/(x(-nf(x(0，构造函数g(x(=

6.对于不等式f/(x(-f(x(0，构造函数g(x(=

7.对于不等式f/(x(+f(x(0，构造函数g(x(=exf(x)

8.对于不等式f/(x(+kf(x(0，构造函数g(x(=ekxf(x)

9.对于不等式f/(x(sinx+f(x(cosx0，构造函数g(x(=sinxf(x)

10.对于不等式f/(x(sinx-f(x(cosx0，构造函数g(x(=

11.对于不等式f/(x(cosx-f(x(sinx0，构造函数g(x(=cosxf(x)

12.对于不等式f/(x(cosx+f(x(sinx0，构造函数g(x(=

重难点题型(一)、与一次函数或幂函数有关的构造函数

1.(23-24高三下·重庆)已知函数f(x(的定义域为(-∞,0(，f(-1(=-1，其导函数f/(x(满足xf/(x(-2f(x(0，则不等式f(x+2025(+(x+2025(20的解集为()

A.(-2026,0(B.(-2026,-2025(C.(-∞,-2026(D.(-∞,-2025(

1

1

2.(2021·安徽高三月考(理))设函数f(x(是定义在(0,+∞(上的可导函数，其导函数为f(x(，且有2f(x(xf(x(，则不等式4f(x-2021((x-2021(2f(2(的解集为()

A.(2021,2023(B.(0,2022(C.(0,2020(D.(2022,+∞(

3.(2022·四川省眉山第一中学模拟预测(理))已知可导函数f(x)的定义域为(0,+∞)，满足xf/(x)-2f(x)0，且f(2)=4，则不等式f(x)x2的解集是.

4.(23-24高三上·云南昆明)已知定义域为R的函数f(x(，对任意的x∈R都有f/(x(2x，且f(1(=2，则不等式f(2x(-4x2-10的解集为()

A.(0,+∞(B.(,+∞(C.(1,+∞(D.(2,+∞(

1.(22-23高三下·广东)已知f(x)是定义在R上的偶函数，当x0时，有xf/(x)+2f(x)0恒成立，则()

A.4f

C.9f((4f(-D.9ff(-

2.(22-23高三下·广东东莞)已知函数f(x(的定义域为(-∞,0(,其导函数f/(x(满足xf/(x(-2f(x(0,则不等式f(x+2023(-(x+2023(2f(-1(0的解集为()

A.(-2024,-2023)B.(-2024,0)C.(-∞,-2023)D.(-∞,-2024)

3.(22-23高三上·山东泰安·阶段练习)已知f(x(是定义在R上的偶函数，f/(x(是f(x(的导函数，当x≥0时，f/(x(-2x0，且f(1(=2，则f(x(x2+1的解集是()

A.(-1,0(∪(1,+∞)B.(-∞,-1(∪