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Unformatted text preview: he weekly proﬁt. Hence, P ◦ p−1 (x)
gives us the weekly proﬁt (in dollars) as a function of the price per system, x, using the weekly
sales p−1 (x) as the ‘middle man’. 4. We know from Section 2.3 that the graph of y = P ◦ p−1 (x) is a parabola opening downwards. The maximum proﬁt is realized at the vertex. Since we are concerned only with the
price per system, we need only ﬁnd the x-coordinate of the vertex. Identifying a = − 2 and
b = 220, we get, by the Vertex Formula, Equation 2.4, x = − 2ba = 165. Hence, weekly proﬁt
is maximized if we set the price at $165 per system. Comparing this with our answer from
Example 2.3.3, there is a slight discrepancy to the tune of $0.50. We leave it to the reader to
balance the books appropriately. 7 It is good review to actually do this! 5.2 Inverse Functions 5.2.1 309 Exercises 1. Show that the following functions are one-to-one and ﬁnd the inverse. Check your answers
algebraically and graphically. Verify the range of f is the domain of f −1 and vice-versa.
(a) f (x)...
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