Find the inverse of f(x) = 9x+2 divided by 3x And give it's domain.

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.