Page 61 - Calculus Demystified

Basics
CHAPTER 1
48 in Fig. 1.54 are the graphs of the inverse functions corresponding to (a) and (b)
of Fig. 1.53 respectively. They are obtained by reflection in the line y = x.

Fig. 1.54

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Fig. 1.55
In Fig. 1.55, graphs (a) and (b) are not the graphs of invertible functions.
For each there is exhibited a horizontal line which intersects the graph twice.
However graphs (a) and (b) in Fig. 1.56 exhibit a way to restrict the domains
of the functions in (a) and (b) of Fig. 1.55 to make them invertible. Graphs (a)
and (b) in Fig. 1.57 show their respective inverses.

Fig. 1.56
You Try It: Give an example of a function from R to R that is not invertible, even
when it is restricted to any interval of length 2.

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