( ) b. = 0 g x − + + 6 = 0 x2 x − − 6 = 0 x2 x ( ( − 3) + 2) = 0 x x = 3; = −2 x x {−2, Solution set: 3} . { } ( ) ( ) The solution set is ≤ −2 or ≥ 3 or, c. = x x x f x g x (−∞, [3, ∪ ∞) − − + 1 = − + x2 x x2 x using interval notation, 2] + 6 . −2 − = 5 x 0 ( ) ( ) > f. −2x = 5 f x g x − − + > − + + 1 6 x2 x x2 x 5 x −2x > Solution set: . ⎧− 5 ⎫ <− x 2 ⎨ 2 ⎬ ⎩ ⎭ ( ) d. > 0 { } f x The solution set is <− or, x x 5 − − + > 1 0 x2 x (−∞, ) interval notation, − . + −1 < 0 x2 x 5 ( ) g. ≥ 1 f x (1) − + ≥ − ± 1 1 x = x − − − x2 x ≥ (1)2 (1) (−1) − 4 (1) 2 0 = −1 ± 1 + 4 = −1 ± ( − + 1) ≥ 0 x x 5 2 2 2 2 ( ) = + − 1 p x x2 x The zeros are The are = −1 and = 0 . = −1 − 5 ≈ −1.62 and = −1 + 5 ≈ x x x x ( ) ( = − + 1) p x x x 0.62 { −∞, The solution set is x } , 2 2 −1 ≤ ≤ 0 or, using x ∞ , 2 2 [−1, interval notation, 0] . −1 − < < −1 + 5 x x The solution set is 5 33. a. The ball strikes the ground when 2 ⎪⎨ ⎪⎬ (t ) = 0 2 2 . = − 80t s 16t ⎛ −1 − 5 −1 + 5 ⎞ 80t − 16t = 0 or, using interval notation, . ⎜ , ⎟ 2 (5 ) − = 16t 0 t ( ) ≤ 0 e. g x
b. g ( x ) = 0 − x2 + x + 6 = 0 x2 − x − 6 = 0 ( x − 3) ( x + 2) = 0 x = 3; x = −2 Solution set: {−2, 3} . c. f ( x ) = g ( x ) − x2 − x + 1 = − x2 + x + 6 −2 x − 5 = 0 −2x = 5 The solution set is { x x ≤ −2 or x ≥ 3 } or, using interval notation, (−∞, 2] ∪ [3, ∞) . f. f ( x ) > g ( x ) − x2 − x + 1 > − x2 + x + 6 5 x −2x > Solution set: ⎧− 5 ⎫ . x <− 2 ⎨ 2 ⎬ ⎩ ⎭ d. f ( x ) > 0 − x2 − x + 1 > 0 x2 + x −1 < 0 The solution set is { x x <− 5 } or, interval notation, (−∞, − 5 ) . g. f ( x ) ≥ 1 − (1) ± x = (1)2 − 4 (1) (−1) − − x + 1 ≥ 1 − x2 − x ≥ 2 (1) = −1 ± 1 + 4 = −1 ± 5 0 − x ( x + 1) ≥ 0 2 2 The zeros are x = −1 − 5 ≈ −1.62 and x = −1 + 5 ≈ 0.62 2 2 p ( x ) = x2 + x − 1 The are x = −1 and x = 0 . p ( x ) = − x ( x + 1) −∞, 2 2 , 2 2 , ∞ The solution set is { x −1 ≤ x ≤ 0 } or, using interval notation, [−1, 0] . The solution set is x −1 − 5 < x < −1 + 5 33. a. The ball strikes the ground when 2 ⎪⎨ 2 2 ⎪⎬ s (t ) = 80t − 16t = 0 . ⎛ −1 − 5 −1 + 5 ⎞ or, using interval notation, ⎜ , ⎟ . 80t − 16t 2 = 0 16t (5 − t ) = 0 e. g ( x ) ≤ 0
Downloadable-Solution-Manual-for-Precalculus-Concepts-Through-1.docx