) = 4x −1; x 32. ( ( ) = −2 + 5 f g x x 35. ( ) = 0 a. f x 4x −1 = 0 = 1 x 4 ( ) b. > 0 f x −1 > 4x 0 > 1 x 4 The solution set is ⎧ > 1 ⎫ or ⎛ 1 , ∞ ⎞ . x x ⎨ ⎬ 4 ⎜ ⎟ 4 ⎩ ⎭ ⎝ ⎠ This is a linear function, since the average rate of ( ) ( ) c. = f x g x = 6 6 x 4 = 1 x x 33. ( ) ( ) d. ≤ f x g x −1 ≤ −2 4 x x = + 5 is 6 ≤ 6 x ≤ 1 x at {x (−∞, ≤ + The solution set is 1} or 1] . x 0.5 5 e. This is a linear function with = 0, since the average rate of change is constant at 0. 36. ( ) = 3x + f x 34. 5; ( ) = −2x + 15 g x ( ) = a. 0 f x 3x + 5 = 0 5 3 = − The x 3 solution set is ⎧ ( ) < b. 0 f x x x 3x + 5 < 0 This is not a linear function, since the average 5 ⎫ or < − 5 rate of change is not constant. x ⎛ − ,
32. 35. f ( x ) = 4x −1; g ( x ) = −2 x + 5 a. f ( x ) = 0 4x −1 = 0 x = 1 4 b. f ( x ) > 0 4x −1 > 0 x > 1 4 The solution set is ⎧ x x > 1 ⎫ or ⎛ 1 , ∞ ⎞ . ⎨ 4 ⎬ ⎜ 4 ⎟ This is a linear function, since the average rate of ⎩ ⎭ ⎝ ⎠ c. f ( x ) = g ( x ) 33. is at 0.5 4 x = + 5 6 x = 6 x = 1 d. f ( x ) ≤ g ( x ) 4 x −1 ≤ −2 x + 5 6 x ≤ 6 x ≤ 1 The solution set is {x x ≤ 1} or (−∞, 1] . e. 34. This is a linear function with = 0, since the average rate of change is constant at 0. 36. f ( x ) = 3x + 5; g ( x ) = −2x + 15 a. f ( x ) = 0 3x + 5 = 0 5 This is not a linear function, since the average rate of change is not constant. x = − 3 b. f ( x ) < 0 3x + 5 < 0 x < − 5 3 The solution set is ⎧ x x 5 ⎫ or ⎛ − ,
Downloadable-Solution-Manual-for-Precalculus-Concepts-Through-1.docx