Question

己知f(x)=ln1/x，x>0，1/x，x<0则f(x)>-1的解集为

答案详细点。。。谢谢

Answer 1

f(x)=ln(1/x) x>0
f(x)=1/x x<0

x<0 f(x)=1/x>-1
1/x+1>0
(1+x)x>0
x>0或x<-1
综上x<-1

x>0 f(x)=ln(1/x)>-1=ln(1/e)
1/x>1/e
1>x/e

e>x
0<x<e

综上x<-1或0<x<e

Answer 2

解:
①
当x>0时
ln1/x>-1
1/x>1/e
所以
0<x<e
②当x<0
1/x>-1
1/x + 1>0
(1+x)/x>0
x∈(负无穷,-1)