已知函数f(x)=ax+x-b的零点x1∈(n,n+1)(n∈Z),其中常数a,b满足2a=3,3b=2,则n等于(  ) A.-1 B.-2 C.1 D.2

问题描述:

已知函数f(x)=ax+x-b的零点x1∈(n,n+1)(n∈Z),其中常数a,b满足2a=3,3b=2,则n等于(  )
A. -1
B. -2
C. 1
D. 2

∵常数a,b满足2a=3,3b=2,
∴a=log23,b=log32,
∴a>1,0<b<1,
∴f(0)=a0+0-b=1-b>0,
f(-1)=a-1-1-b=log32-1-log32=-1,
∵f(-1)•f(0)<0,
∴零点x1∈(-1,0),
∵x1∈(n,n+1)(n∈Z),
∴n=-1,
故选:A