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Example 2: The Reciprocal Function

The reciprocal function g is given by the rule


g(x) is defined for all nonzero x, but is undefined at x = 0. Find the following values if they are defined: g(0), g(2), g(-⅓), g(7/4), g(r + 1).

01_real_and_hyperreal_numbers-24.gif, 01_real_and_hyperreal_numbers-25.gif, 01_real_and_hyperreal_numbers-26.gif.

01_real_and_hyperreal_numbers-27.gif, 01_real_and_hyperreal_numbers-28.gif

The graph of the reciprocal function has the equation y = 1/x. This equation can also be written in the form xy = 1. The graph is shown in Figure 1.2.4.


Figure 1.2.4

Last Update: 2006-11-09