How do you find the domain and inverse of $f(x)=ln(3+ln(x))$ ?

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Answer 1 · 2016-07-02T10:21:18

$x>e^(-3)>0.0497871$ , nearly..
$x=0.0497871 (e^(e^f))$ , nearly

For f to be real,

$3+ln x>0$ . So, $ln x>-3$ . And so, $x>e^(-3) >0.0497871$ , nearly.

Inversion:

$e^f=3+ln x.$

$So, ln x = e^f-3.$

And so, $x=e^(e^f-3)=e^(-3)e^(e^f)= 0.0497871 e^(e^f)$

How do you find the domain and inverse of f(x)=ln(3+ln(x))f(x)=ln(3+ln(x))?