Answer:
[tex]y = \frac{2x}{x - 1} [/tex]
Step-by-step explanation:
find the inverse of the function
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables
[tex]y = \frac{x}{x - 2} [/tex]
becomes
[tex]x = \frac{y}{y - 2} [/tex]
Now, solve the equation
[tex]x = \frac{y}{y - 2} [/tex]
for y.
[tex]y = \frac{2x}{x - 1} [/tex]
