SOLUTION: Find the domain of f(x)= ln (e^x - 3). Find f-1 and its doman

Question 895198: Find the domain of f(x)= ln (e^x - 3). Find f-1 and its doman
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the domain of f(x)= ln (e^x - 3). Find f-1 and its doman
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Domain::
y = ln(e^x-3)
1st:: e^x-3 must be > 0
2nd: Solve for "x"::
e^x - 3 > 0
e^x > 3
x > ln(3)
That is the domain for f(x)
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Find f^-1(x)
y = ln(e^x-3)
1st:: Interchane x and y to get:
x = ln(e^y-3)
2nd: Solve for "y"::
e^y - 3 = e^x
----
e^y = e^x+3
y = ln(e^x+3)
That is f^-1(x)
====================
Cheers,
Stan H.
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