Question 1163140
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The answer from the other tutor demonstrates the standard way of finding the inverse of a function, which you were trying to do.<br>
For many functions, it is easy to find an inverse by using the idea that an inverse function "un-does" what the function does.<br>
Using that concept, the inverse function has to perform the opposite operations, and in the reverse order, compared to the original function.<br>
The given function does the following to the input value:
(1) raise e to that power
(2) subtract 2
(3) take the square root
(4) take the natural log<br>
The inverse function must then
(1) raise e to the power
(2) square it
(3) add 2
(4) take the natural log<br>
That sequence of operations gives us the inverse function:<br>
{{{x}}} --> {{{e^x}}} --> {{{(e^x)^2 = e^(2x)}}} --> {{{e^(2x)+2}}} --> {{{ln(e^(2x)+2)}}}<br>