x-2/3x+1,determine the inverse.
x= y-2/3y+1
x (3y+1)=y-2
3xy+x=y-2
(where do i go from here if i am going right)
To determine the inverse of the function, we need to solve for y. Let's continue solving the equation:
3xy + x = y - 2
First, let's move all the terms involving y to one side of the equation:
3xy - y = -x - 2
Next, factor out the common y term:
y(3x - 1) = -x - 2
Finally, divide both sides of the equation by (3x - 1) to isolate y:
y = (-x - 2)/(3x - 1)
Therefore, the inverse of the function is:
f^-1(x) = (-x - 2)/(3x - 1)