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(a) Find the domain of $f(x)=\ln \left(e^{x}-3\right)$(b) Find $f^{-1}$ and its domain.

(a) $(\ln 3,+\infty)$(b) $f^{-1}(x)=\ln \left(e^{x}+3\right) ;$ Domain: $(-\infty, \infty)$

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

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University of Michigan - Ann Arbor

University of Nottingham

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this question asked us to find the domain and then the inverse. We know that half of axe is natural log of each The power of X minus three. We know that natural log of each. The power of acts has to be greater than natural. Order three and then taking away the natural walk we end up with acts is greater than natural either three Because remember natural. I'm Tensy cancels off the left inside, leaving us with natural log of three times comma positive. Infinity is our coordinates for the domain. A second part of this problem is the inverse. We can't take E as our base or common base for both sides and then natural log of each. The why is natural log of eat the ax plus three. Allowing us to write inverse function of acts is not your log of each the ax plus three and the domain is all real numbers which you can write like this or from negative infinity to positive infinity

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