Math 023 Fall 2022 100722 Inverse Functions
Leftovers from 3.4 and 3.5: example of function with a translation and a reflection; iterating functions.
3.6: Inverse functions. Motivation: Q. Is this the graph of a function? Q. Is the flipped (across y=x) graph of a function always the graph of a function? Not always: the graph must pass the "horizontal line test." Q. If it is, what is the relationship between the two functions? A. One sees that they "undo" each other's actions. Formal definition of inverse functions, using composition. Examples. Q. How does one solve for the inverse function? Trivial answer: solve f(x)=y for x; that will be the inverse function (in y). Examples.
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