Question

若函數(shù)y=ax+2的圖象與函數(shù)y=

1

2

x-

b

4

的圖象關(guān)于直線y=x對(duì)稱，則log_ab的值是（　�。�

A．- 1 2

B． 1 2

C．1

D．2

Answer 1

∵y=ax+2的圖象與y=

1

2

x-

b

4

的圖象關(guān)于直線y=x對(duì)稱，
∴y=ax+2圖象上任一點(diǎn)P（x，ax+2）關(guān)于y=x對(duì)稱點(diǎn)Q（ax+2，x）必在y=

1

2

x-

b

4

的圖象上．
故對(duì)一切實(shí)數(shù)x總有x=

1

2

(ax+2)-

b

4

，
∴

1= 1 2 a 0=1- b 4

?

a=2 b=4

．
則log_ab=則log₂4=2．
故選D．