Question 1153262
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Tutor @MathLover1 has shown finding the inverse by the traditional formal algebraic method -- switching the x and y and solving for the new y.<br>
For many relatively simple functions, it is far easier to find the inverse using the idea that an inverse "gets you back where you started from".<br>
To "get you back where you started from", an inverse function has to perform the opposite operations in the opposite order, compared to the original function.<br>
In this example, the function does the following operations on the input:
(1) multiply by 3
(2) subtract 5/2<br>
So the inverse function has to
(1) add 5/2
(2) divide by 3<br>
So the inverse function is {{{(x+5/2)/3 = (1/3)x + 5/6}}}<br>
Much less work than the formal algebraic method....<br>