函数f(x)的定义域为D,若满足: ①f(x)在D内是单调函数; ②存在[a,b]⊆D,使f(x)在[a,b]上的值域为[-b,-a],那么y=f(x)叫做对称函数. 现有f(x)=2−x-k是对称函数,那么k的取值范
函数f(x)的定义域为D,若满足:
①f(x)在D内是单调函数;
②存在[a,b]⊆D,使f(x)在[a,b]上的值域为[-b,-a],那么y=f(x)叫做对称函数.
现有f(x)=
-k是对称函数,那么k的取值范围是( )
A. [2,
)
B. (-∞,
)
C. (2,
)
D. (−∞,
](-∞,
]
①f(x)在D内是单调函数;
②存在[a,b]⊆D,使f(x)在[a,b]上的值域为[-b,-a],那么y=f(x)叫做对称函数.
现有f(x)=
2−x |
A. [2,
9 |
4 |
B. (-∞,
9 |
4 |
C. (2,
9 |
4 |
D. (−∞,
9 |
4 |
9 |
4 |
数学人气:775 ℃时间:2020-03-24 14:31:44
优质解答
由于f(x)=2−x在(-∞,2]上是减函数,故满足①,又f(x)在[a,b]上的值域为[-b,-a],∴2−a−k=−a2−b−k=−b∴a和 b 是关于x的方程2−x在(-∞,2]上有两个不同实根.令t=2−x在,则x=2-t2,t≥0,∴k=-t2+...
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