Solving inequalities (§5.4)

There is a very general technique for solving inequalities in one variable that applies to expressions built using pretty much all of the functions that we consider in this course. Specifically, it applies to all piecewise continuous functions. Exactly what that means is generally explained in a Calculus course, but I can already tell you what examples we have of these: any function made of the following operations is piecewise continuous: Because of the fine print, there are potential exceptions here; if I want to solve (−2)x < 1, for example, then I can do it, but not by this method directly. But of course, that's exactly the sort of exponential function that we refused to consider in Section 6.3!

Here is the method:

For rational functions, this method is in the textbook, but it still applies to other expressions, such as those inolving roots (of constant index) or logarithms.
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This web page was written in 2015 by Toby Bartels, last edited on 2015 December 8. Toby reserves no legal rights to it.

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