Question

若f(x)是R上的減函數(shù),且f(x)的圖象經(jīng)過點(diǎn)A(0,4)和點(diǎn)B(3,-2),則不等式|f(x+a)-1|<3的解集為(-1,2)時(shí),a的值為

1. A.
   0
2. B.
   -1
3. C.
   1
4. D.
   -2

Answer 1

C
由|f(x+a)－1|<3,得－2<f(x+a)<4.
由題設(shè)可知f(0)=4,f(3)=－2.
所以f(3)<f(x+a)<f(0).
又因f(x)是R上的減函數(shù),所以0<x+a<3,
即－a<x<3－a.                                                                                                       ①
因不等式的解為－1<x<2,                                                                                       ②
所以比較①②可得a=1.