Question

Find the domain of f(x)=ln(1+lnx)
Find the inverse of f(x) and its domain.

Answer 1

the domain of the log is positive reals, i.e. \(x>0\) so in order for the outside function to exist, it must be the case that \(1+\ln(x)>0\) and \(x>0\)

Answer 2

right, so for f(x), x.0, got that part

Answer 3

\(1+\ln(x)>0\implies \ln(x)>-1\implies x>e^{-1}=\frac{1}{e}\)

Answer 4

x>0

Answer 5

which is your final answer, because if \(x>\frac{1}{e}\) it is already greater than zero

Answer 6

whats the equation for the inverse function though?

Answer 7

@satellite73