Question 1196625
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The response from the other tutor shows the method which is usually taught for finding the inverse of a function: switch the x and y and solve for the new y.<br>
Another method which is often easier is to use the idea that an inverse function "un-does" what the function does.<br>
The given function does the following to the input variable:<br>
{{{x}}}
(1) subtract 4 --> {{{x-4}}}
(2) multiply by -1 --> {{{4-x}}}
(3) raise e to that power --> {{{e^(4-x)}}}<br>
The inverse function must do the opposite operations, in the opposite order:<br>
{{{x}}}
(1) take natural log --> {{{ln(x)}}}
(2) multiply by -1 --> {{{-ln(x)}}}
(3) add 4 --> {{{-ln(x)+4}}}<br>
ANSWER: The inverse function is {{{y=-ln(x)+4}}}<br>