The function f is defined as f(x)=(2x+1)/(x-3). Find the value of k so that the inverse of f is f^-1(x)=(3x+1)/(x-k).

We'll determine the inverse function
f^-1(x).

Let f(x)=y, such
as:

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

We'll
multiply both sides by (x-3):

xy - 3y =
2x+1

We'll move 3y to the
right:

xy = 2x + 3y +1

We'll
subtract 2x both sides:

xy - 2x = 3y +
1

We'll factorize by x to the
left:

x(y - 2) = 3y + 1

We'll
divide by (y-2):

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

The inverse function is: f^-1(x) =
(3x+1)/(x-2)

Comparing with the given
expression of f^-1(x) = (3x+1)/(x-k), we'll identify k =
2.