A Function `f(x)` is defined as: `f(x) = {3x-1}/{x-2}`, x not equal to 2, evaluate `f^-1 (5)`

Solution:

To evaluate `f^(-1)(5)`, we need to find the inverse function of `f(x)` and then substitute 5 into it.

Let's start by finding the inverse function of `f(x)`:

`f(x) = {3x-1}/{x-2}`

Swap x and y: 

`x = {3y-1}/{y-2}`

Solve for y:

Multiply both sides by (y-2): 

`x(y-2) = 3y - 1`

Distribute: 

`xy - 2x = 3y - 1`

Move all terms involving y to one side: 

`xy - 3y = 2x - 1`

Factor out y: 

`y(x - 3) = 2x - 1`

Divide both sides by (x - 3): 

`y = (2x - 1)/(x - 3)`

So, `f^-1 (x) = (2x - 1)/(x - 3)`

Now, let's substitute 5 into `f^-1 (x)` to find the value of `f^-1 (5)`:

`f^-1 (5) = (2 * 5 - 1)/(5 - 3)`

`f^-1 (5) = (10 - 1)/(2)`

`f^-1 (5) = 9/2`

Therefore, the value of `f^-1 (5)` is `9/2`.