Question 1205754
<br>
The other tutor shows what is probably the standard method for finding the inverse of a function.<br>
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".<br>
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.<br>
For this example, the sequence of operations performed on the input x is
(1) subtract 2: {{{x-2}}}
(2) exponentiation with base e: {{{e^(x-2)}}}
(3) multiply by 2: {{{2e^(x-2)}}}<br>
The inverse function must perform the opposite operations in the opposite order:
(1) divide by 2: {{{x/2}}}
(2) take the natural log: {{{ln(x/2)}}}
(3) add 2: {{{ln(x/2)+2}}}<br>
Note the format of the inverse function is different than the one shown by the other tutor; but the two forms are equivalent.<br>
ANSWER: The inverse function is {{{ln(x/2)+2}}}<br>