298 CHAPTER 2 Graphs and Functions SOLUTION (a) 1ƒ + g21x2 = ƒ1x2 + g1x2 = 8x - 9 + 22x - 1 (b) 1ƒ - g21x2 = ƒ1x2 - g1x2 = 8x - 9 - 22x - 1 EXAMPLE 2 Using Operations on Functions Let ƒ1x2 = 8x - 9 and g1x2 = 22x - 1. Find each function in parts (a)–(d). (a) 1ƒ + g21x2 (b) 1ƒ - g21x2 (c) 1ƒg21x2 (d) a f gb1x2 (e) Give the domains of the functions in parts (a)–(d). EXAMPLE 1 Using Operations on Functions Let ƒ1x2 = x2 + 1 and g1x2 = 3x + 5. Find each of the following. (a) 1ƒ + g2112 (b) 1ƒ - g21-32 (c) 1ƒg2152 (d) a ƒ gb102 SOLUTION (a) First determine ƒ112 = 2 and g112 = 8. Then use the definition. 1ƒ + g2112 = ƒ112 + g112 1ƒ + g21x2 = ƒ1x2 + g1x2 = 2 + 8 ƒ112 = 12 + 1; g112 = 3112 + 5 = 10 Add. (b) 1ƒ - g21-32 = ƒ1-32 - g1-32 1ƒ - g21x2 = ƒ1x2 - g1x2 = 10 - 1-42 ƒ1-32 = 1-322 + 1; g1-32 = 31-32 + 5 = 14 Subtract. (c) 1ƒg2152 = ƒ152 # g152 1ƒg21x2 = ƒ1x2 # g1x2 = 152 + 1213 # 5 + 52 ƒ1x2 = x2 + 1; g1x2 = 3x + 5 = 26 # 20 ƒ152 = 26; g152 = 20 = 520 Multiply. (d) a ƒ gb102 = ƒ102 g102 A ƒ gB1x2 = ƒ1x2 g1x2 = 02 + 1 3102 + 5 ƒ1x2 = x2 + 1 g1x2 = 3x + 5 = 1 5 Simplify. S Now Try Exercises 11, 13, 15, and 17.
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