Question

设f(x)=lnx,g(x)=2(x+1)/x-1,则f[g-1(x)]=?

Answer 1

答：

y=g(x)=2(x+1)/(x-1)

=2(x-1+2)/(x-1)

=2+4/(x-1)

y-2=4/(x-1)

x-1=4/(y-2)

所以：

g-1(x)=1+4/(x-2)=(x+2)/(x-2)

因为：

f(x)=lnx

所以：f [g-1(x) ]=ln [(x+2)/(x-2)]