Question 1181200
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You have received two responses from tutors so far that both use the same method for finding the inverse of a function: switch the x and y and solve for the new y.<br>
That is a standard method which you should know and understand.<br>
For many relatively simple functions like this one, the inverse can be found more easily, without algebra, using the notion that an inverse function "un-does" what the function does.<br>
In this example, the operations performed on the input by the given function are
(1) raise it to the 3rd power;
(2) multiply by 2; and
(3) add 1<br>
The inverse function must undo those operations by performing the opposite operations in the opposite order:
(1) subtract 1:  {{{x-1}}}
(2) divide by 2:  {{{(x-1)/2}}}
(3) take the cube root:  {{{root(3,(x-1)/2)}}}<br>
If you compare that informal method for finding the inverse to the formal mathematical method shown by the other tutors, you will see that EXACTLY the same work is being done; however, the path to the solution is easier and faster without the need for the formal algebra.<br>