The response from the other tutor shows a standard formal method for finding the inverse of a function.
For many functions for which an inverse exists, another method which is often faster is to use the idea that an inverse function "gets you back where you started from".
The given function does the following to the input x to get the function value:
(1) multiply by 2 [x --> 2x]
(2) take the reciprocal [2x --> 1/(2x)]
(3) add 3 [1/(2x) --> 1/(2x)+3]
The inverse must perform the inverse operations in the reverse order:
(1) subtract 3 [x --> x-3]
(2) take the reciprocal [x-3 --> 1/(x-3)]
(3) divide by 2 [1/(x-3) --> 1/(2(x-3))]
