设f(x)=1,当lxl1 求f[g(x)]和g[f(x)],

题目

设f(x)=1,当lxl1 求f[g(x)]和g[f(x)],

答案

le^xl<1<=>x<0.
le^xl=1<=>x=0.
le^xl>1<=>x>0.
f[g(x)]={1(x<0),0(x=0),-1(x>0)}
g[f(x)]=e^f(x)={e(lxl<1),1(lxl=1),1/e(lxl>1)}