Description
Assigned Problems from Chapter 3 (12 total problems):
Exercise Set 3.5 Pages 285-286 Problems: 2, 6, 22, 28
Exercise Set 3.6 Pages 296-300 Problems: 10, 20, 24, 36
Exercise Set 3.7 Pages 306-308 Problems: 4, 10, 28, 38
Assigned Problems from Chapter 6 (3 total problems):
Exercise Set 6.1 Pages 505-508 Problems: 26, 48, 64
Explanation & Answer
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Page 329, #40. 𝒇(𝒙) = −𝒙𝟑 + 𝟒
Getting the inverse of the function, we first replace f(x) into y.
𝑦 = −𝑥 3 + 4
Then, we replace all x into y and all y into x.
𝑥 = −𝑦 3 + 4
Next, solve for y.
𝑥 = −𝑦 3 + 4
𝑦3 = 4 − 𝑥
3
𝑦 = √4 − 𝑥
Finally, we replace y into 𝑓 −1 (𝑥).
𝟑
𝒇−𝟏 (𝒙) = √𝟒 − 𝒙
Graphing 𝑓(𝑥) and 𝑓 −1 (𝑥):
3
Fig. 1.1. Graph of 𝑓(𝑥) = −𝑥 3 + 4 and 𝑓 −1 (𝑥) = √4 − 𝑥.
Page 331, #76. The Universal Product Code or UPC is a symbology with barcode and numbers that is
used to identify the type, brand, price and other information about a product. The product is a function
of the UPC because his makes products easier to be identified and faster for sellers to know the price. All
functions have inverses. Not all inverse of any function is also a function unless it passes the horizontal
line test.
Page 341, #46. 𝒈(𝒙...
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