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

1 Answer

A. S. Adikesavan

Jul 2, 2016

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

Explanation:

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)#

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