Solve this problem in two steps.
Step 1
Express x via y:
ln(y) = ln(2) +
ln(y) = ln(2) + (x-2)
x =
x = .
Step 2
Now swap in this equation x and y
y = .
The last expression represents the inverse function.
The other tutor shows what is probably the standard method for finding the inverse of a function.
For many relatively simple functions, the inverse can be found informally using the concept that the inverse of a function "gets you back where you started".
For the inverse of the given function to get you back where you started, it has to perform the opposite operations as the given function, and in the opposite order.
For this example, the sequence of operations performed on the input x is
(1) subtract 2:
(2) exponentiation with base e:
(3) multiply by 2:
The inverse function must perform the opposite operations in the opposite order:
(1) divide by 2:
(2) take the natural log:
(3) add 2:
Note the format of the inverse function is different than the one shown by the other tutor; but the two forms are equivalent.
