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Find the inverse of f(x) = 9x+2 divided by 3x

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1 Answer

Let's start with f(x).
 
f(x)=(9x+2)/3x  with a domain of all real number except 0.   (we cannot have 0 at the denominator)
 
 
In order to find out the inverse, set the function =y, and solve for x
 
(9x+2)/3x=y/1
 
Let's cross multiply (you'll see it more easily if you write it down on paper)
 
9x+2=3xy
 
Let's separate the terms that have x's from all the other numbers/variables:
 
9x-3xy=-2
 
x(9-3y)=-2
 
x=-2/(9-3y)      And there you go, the inverse is 9-3y, however.. we generally report the inverse with the same variable so:
 
 
f-1(x)=-2/(9-3x)        with a domain of all real numbers except 3. Why 3? the denominator is not allowed to be 0, as we cannot divide by 0.
 
therefore, 9-3x cannot equal 0, so x cannot equal 3.

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