Question 1132798
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For relatively simple functions, there is a way to find the inverse that is nearly always much faster than switching the x and y and solving for the new y.<br>
The method is based on the general concept that an inverse function "gets you back where you started".<br>
For an inverse function to get you back where you started, the operations it performs must be the opposite operations from what the function does, and in the reverse order.<br>
In your example, the operations the function performs on the input value are
(1) add 2
(2) raise to the 5th power
(3) add 3<br>
The opposite operations, in the opposite order, are
(1) subtract 3
(2) take the 5th root
(3) subtract 2<br>
That gives you, as the inverse function,<br>
{{{y = (x-3)^(1/5)-2}}}