Answer to Question #16955 in Calculus for hsd

Question

Find (a) the domain of f and (b) f−1.
f(x)=ln(2+lnx)

(a) x>............
(b) f−1(x)=...........

Answer 1

a) ln x so x>0 in other hand 2+ln(x)>0 so ln(x)>-2 so
x>e^(-2)>0
x>e^(-2)
b)f^(-1) can be defined on every point
because for every y y=ln(2+ln(x)) have exactly one solution
e^y=2+ln(x)

ln(x)=e^y-2
x=e^[ e^y-2 ]