Final answer:
The inverse of the function g(x) = 2x/(x-3) is f(x) = (3x)/(x - 2).
Step-by-step explanation:
The inverse of the function g(x) = 2x/(x-3) can be found by switching the variables x and y and then solving for y. Let's start by switching the variables:
x = 2y/(y-3)
Next, we can cross-multiply to eliminate the denominator:
x(y-3) = 2y
Expand the left side of the equation:
xy - 3x = 2y
Now, let's isolate y:
xy - 2y = 3x
Factoring out y:
y(x - 2) = 3x
Dividing both sides by (x - 2):
y = (3x)/(x - 2)
Therefore, the inverse of the function g(x) = 2x/(x-3) is f(x) = (3x)/(x - 2).