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ƒ{ƒ‹ƒgƒƒX —ìb ‰»g ˆá‚¢-G(x) is the set of all real numbers Also, g(g(x)) is defined for the set of all real numbers Therefore, the domain of D g g is the set of all real numbers Example 3 Evaluate the expression D g f ( )(4) if = g x x −( ) 16 3 and 1 ( ) x f x = Solution There are a couple of ways to work a problem like this We can either evaluate f(x) at the value x = 4, then substitute thisThen Player I has a winning strategy in G(X) consisting in playing always b There are other possible winning strategies for Player I For example, she can play systematically a when Player II plays b and conversely This example shows that the winning strategy is not unique in general In the games considered in this chapter, all plays are infinite In the games of everyday life, the plays
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