Functions and Algebra: Explanation

When reversing the effect of a function which is expressed in several steps, we must 

While you may not have thought of reversing the steps, at first, a concrete example will make this very clear.  Think about the process of getting dressed.  For the "getting dressed" function, you (without clothes) are the input and the some of the steps are:

The reverse function, "getting undressed", takes you with clothes as the input, and requires the steps:

It is clear that, if you tried to do this in the other order it would not work!  Aside: It is interesting to note that, while this is now intuitive to you, much of the experimentation that small children perform revolves around learning this basic, mathematical fact!


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