函数y=f(x)在(-2,0)上是减函数,函数y=f(x-2)是偶函数,则()A.f(-103)<f(-73)<f(-43)B.f(-43)<f(-103)<f(-73)C.f(-103)<f(-43

题目简介

函数y=f(x)在(-2,0)上是减函数,函数y=f(x-2)是偶函数,则()A.f(-103)<f(-73)<f(-43)B.f(-43)<f(-103)<f(-73)C.f(-103)<f(-43

题目详情

函数y=f(x)在(-2,0)上是减函数,函数y=f(x-2)是偶函数,则(  )
A.f(-
10
3
)<f(-
7
3
)<f(-
4
3
B.f(-
4
3
)<f(-
10
3
)<f(-
7
3
C.f(-
10
3
)<f(-
4
3
)<f(-
7
3
D.f(-
7
3
)<f(-
10
3
)<f(-
4
3
题型:单选题难度:偏易来源:不详

答案

∵函数y=f(x)在(-2,0)上是减函数,函数y=f(x-2)是偶函数
∴函数关于x=-2对称,数在(-4,-2)是一增函数,
∴自变量离x=-2的距离越近,函数值越大,
由于-class="stub"10
3
,-class="stub"4
3
,-class="stub"7
3
都在(-4,0)上,且|-class="stub"10
3
+2|>|-class="stub"4
3
+2|>|-class="stub"7
3
+2|
∴f(-class="stub"10
3
)<f(-class="stub"4
3
)<f(-class="stub"7
3

故选C

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