4 ( ) e. ≤ g x 0 ( ) = 0 b. g x 4x + 1 ≤ − − 2 = 0 x 0 − = 2 x 4x ≤ −1 = −2 x 1 x ≤− {−2} Solution set: . ⎧ ( ) ( ) The solution set is x x = c. f x g x 1 ⎫ or, using ⎨ ≤− ⎬ ⎩ ⎭ 4 − + 4 = − − 2 ⎛ −∞, − ⎤ interval notation, 1 . x2 x = − − 0 6 x2 x ⎜ 4 ⎥ = 3; = −2 x x ⎝ ⎦ {−2, Solution set: 3} . ( ) ( ) f. > f x g x ( ) d. > 0 f x − + > + 1 4x 1 x2 0 > + 4x x2 − + 4 > x2 ( 0 > + 4) x x 0 − > 4 0 The zeros are = and = 0 . x2 x x –4 (2 ) (2 ) ( ) ( − + > 0 x x = + 4) p x x x The are = and = 2 . x x –2 ( ( 0 = − 3) + 2) x x } { − < < 2 2 or, x The solution set is x { The solution set is x − 4 < < 0} or, using x (−4, interval notation, 0) . (−2, using interval notation, 2) . ( ) g. ≥ 1 f x ( ) ≤ e. 0 g x − + 1 ≥ 1 x2 − − 2 ≤ 0 − ≥ 0 x x2 − ≤ 2 x ≤ 0 x2 ≥ −2 x The zero is = 0 . { x set is ≥ −2} or, using x x [−2, ) interval notation, ∞ . The ( ) = p x x2 ( ) ( ) f. > f x g x − + 4 > − − 2 x2 x 0 > − − 6 x2 x {0} The solution set is . ( ( 0 > − 3) + 2) x x The zeros are = and = 3 . x x –2 ) = − + 4; 28. ( ) ( )( ) x2 ( ) − = g x x ( − 2 f x
e. g ( x ) ≤ 0 4x + 1 ≤ 0 4x ≤ −1 x 1 ≤− 4 b. g ( x ) = 0 − x − 2 = 0 − x = 2 x = −2 Solution set: {−2} . The solution set is ⎧ x x 1 ⎫ or, using c. f ( x ) = g ( x ) ⎨ ≤− ⎬ ⎩ 4 ⎭ interval notation, ⎛ −∞, − 1 ⎤ . − x2 + 4 = − x − 2 0 = x2 − x − 6 ⎜ 4 ⎥ ⎝ ⎦ f. f ( x ) > g ( x ) − x2 + 1 > 4x + 1 0 > x2 + 4x 0 > x ( x + 4) The zeros are x = –4 and x = 0 . p ( x ) = x ( x + 4) 0 = ( x − 3) ( x + 2) x = 3; x = −2 Solution set: {−2, 3} . d. f ( x ) > 0 − x2 + 4 > 0 4 − x2 > 0 (2 − x ) (2 + x ) > 0 The are x = –2 and x = 2 . The solution set is { x − 4 < x < 0} or, using The solution set is { x − 2 < x < 2 } or, interval notation, (−4, 0) . g. f ( x ) ≥ 1 − x2 + 1 ≥ 1 − x2 ≥ 0 x2 ≤ 0 using interval notation, (−2, 2) . e. g ( x ) ≤ 0 − x − 2 ≤ 0 − x ≤ 2 x ≥ −2 The zero is x = 0 . p ( x ) = x2 The set is { x x ≥ −2} or, using interval notation, [−2, ∞ ) . f. f ( x ) > g ( x ) − x2 + 4 > − x − 2 0 > x2 − x − 6 The solution set is {0} . 0 > ( x − 3) ( x + 2) The zeros are x = –2 and x = 3 . 28. f ( x ) = − x2 + 4; g ( x ) = − x − 2 ( ) ( )( )
Downloadable-Solution-Manual-for-Precalculus-Concepts-Through-1.docx