how do i find the inverse of f(x)= (3x+7)/(x-2)

The subject is spelled precalculus.

Let's call f(x) y, and then express x in terms of y.

y = (3x +7)/(x-2)
xy - 2y = 3x + 7
x(y-3) = 7+2y
x = (7+2y)/(y-3)

Finally, call this the "inverse function of x" by changing variables

f^(-1)(x) = (7+2x)/(x-3)

It is the function which will give you x back if you plug in f(x).

Oh sorry, haha thank you for correcting me and thank you for helping me out.

To find the inverse of a function, you need to follow a step-by-step process. Here's how you can find the inverse of the function f(x) = (3x + 7)/(x - 2):

1. Start by replacing f(x) with y: y = (3x + 7)/(x - 2).
2. Swap the x and y variables: x = (3y + 7)/(y - 2).
3. Solve the equation for y. Multiply both sides of the equation by (y - 2) to eliminate the denominator: x(y - 2) = 3y + 7.
4. Distribute on the left side of the equation: xy - 2x = 3y + 7.
5. Rearrange the terms to isolate the y variable on one side: 3y - xy = -2x - 7.
6. Now we can solve for y. Start by moving all terms containing y to one side of the equation: 3y - xy = -2x - 7.
Add xy to both sides: 3y = xy - 2x - 7.
Subtract xy from both sides: 3y - xy = -2x - 7 - xy.
Factor out y on the left side: y(3 - x) = -2x - 7.
Finally, divide both sides by (3 - x) to solve for y: y = (-2x - 7)/(3 - x).

The equation y = (-2x - 7)/(3 - x) is the inverse of the function f(x) = (3x + 7)/(x - 2).