SOLUTION: what is the inverse of f(x) = 4-ln(x+2) ? what is the domain of the inverse function?

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Question 912101: what is the inverse of f(x) = 4-ln(x+2) ?
what is the domain of the inverse function?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the inverse of f%28x%29+=+4-ln%28x%2B2%29

remember that f%28x%29+=y

y+=+4-ln%28x%2B2%29+ ...swap x and y to find the inverse:
x=+4-ln%28y%2B2%29 ....solve for y
ln%28y%2B2%29=+4-x

by definition: log%28a+%2Cx+%29=+N means that a%5EN=+x

in ln%28y%2B2%29 ,you have that a=e, x=y%2B2, and N=4-x

so, e%5E%284-x%29=+y%2B2

+y=e%5E%284-x%29-2
since f%5E%28-1%29%28x%29=y, we have
f%5E%28-1%29+%28x%29+=e%5E%284-x%29-2
or
f%5E%28-1%29+%28x%29+=+-e%5E%28-x%29+%282e%5Ex-e%5E4%29
domain: R (all real numbers)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4-ln%28x%2B2%29%2C+e%5E%284-x%29-2%2Cx%29+