函数f(x)=log2x+2x-1的零点必落在区间(  ) A.(18,14) B.(14,12) C.(12,1) D.(1,2)

问题描述:

函数f(x)=log2x+2x-1的零点必落在区间(  )
A. (

1
8
1
4

B. (
1
4
1
2

C. (
1
2
,1)
D. (1,2)

∵f(

1
8
)=log2
1
8
+2×
1
8
-1=
1
4
-4<0
f(
1
4
)=log2
1
4
+2×
1
4
-1=
1
2
-3<0
f(
1
2
)=log2
1
2
+2×
1
2
-1=1-2<0
f(1)=log21+2×1-1=2-1>0
f(2)=log22+2×2-1=5-1>0
故函数f(x)=log2x+2x-1的零点必落在区间(
1
2
,1)
故选C