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1 answer:
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Answer:
a) The domain of f(x) is .
b)
The inverse function is:
So we need
Applying ln to both sides
So the domain of f(x) is .
(b) Find F −1 and its domain.
is the inverse function of f.
How do we find the inverse function?
To find the inverse equation, we change y with x to form the new equation, and then we isolate y in the new equation. So:
Original equation:
f(x) = y = \ln{e^{x} - 3}
New equation
Here, we apply the exponential to both sides:
Applying ln to both sides
The inverse function is:
The domain is
is always a positive number, so it is always going to be larger than -3 no matter the value of x. So the domain are all the real values.