Page 60 - Calculus Demystified

Basics
CHAPTER 1
In Fig. 1.51, the fact that the line y = 2 intersects the graph twice means that 47
the function f takes the value 2 at two different points of its domain (namely at
x =−2 and x = 6). Thus f is not one-to-one so it cannot be invertible. Figure 1.52
shows what happens if we try to invert f : the resulting curve is not the graph of a
function.

Fig. 1.52

EXAMPLE 1.45
Look at Figs. 1.53 and 1.55. Are the functionswhose graphsare shown in
parts (a) and (b) of each figure invertible?

Fig. 1.53

SOLUTION
Graphs (a) and (b) in Fig. 1.53 are the graphs of invertible functions since
no horizontal line intersects each graph more than once. Of course we must
choose the domain and range appropriately. For (a) we take S =[−4, 4] and
T =[−2, 3]; for (b) we take S = (−3, 4) and T = (0, 5). Graphs (a) and (b)