f(x)=9^x-3^(x+2)
=3^2x-3^x*3^2
=3^2x-9*3^x+81/4-81/4
=(3^x-9/2)^2-81/4
(3^x-9/2)^2=f(x)+81/4
3^x-9/2=±√[f(x)+81/4]
3^x=9/2±√[f(x)+81/4]
lg3^x=xlg3=lg{9/2±√[f(x)+81/4]}
x=lg{9/2±√[f(x)+81/4]}/lg3
所以f(x)的反函数是
f^-1(x)=lg{9/2±√[x+81/4]}/lg3
f^-1(0)=lg{9/2±√[0+81/4]}/lg3
=lg(9/2±9/2)/lg3
当为负时无解,则
原式=lg(18/9)/lg3=lg9/lg3=lg3^2/lg3=2