College Algebra, 2013a

88 Relations and Functions
7. For f(x) =2x and g(x) = 1
2x+1
ˆ (f + g)(2) = 21
5
ˆ (f − g)(−1) = −1 ˆ (g − f)(1) = − 5 3
ˆ (fg) ( ) ( )
( )
1
2 =
1
f
2 ˆ
g
(0) = 0 g
ˆ
f
(−2) = 1
12
8. For f(x) =x 2 and g(x) = 3
2x−3
ˆ (f + g)(2) = 7 ˆ (f − g)(−1) = 8 5
ˆ (g − f)(1) = −4
ˆ (fg) ( ) ( )
( )
1
2 = −
3
f
8 ˆ
g
(0) = 0 g
ˆ
f
(−2) = − 3
28
9. For f(x) =x 2 and g(x) = 1 x 2
ˆ (f + g)(2) = 17
4
ˆ (fg) ( 1
2)
=1 ˆ
10. For f(x) =x 2 + 1 and g(x) = 1
x 2 +1
ˆ (f + g)(2) = 26
5
ˆ (fg) ( 1
2)
=1 ˆ
11. For f(x) =2x + 1 and g(x) =x − 2
ˆ (f − g)(−1) = 0 ˆ (g − f)(1) = 0
( )
( )
f
g
(0) is undefined. g
ˆ
f
(−2) = 1
16
ˆ (f − g)(−1) = 3 2
( )
f
g
(0) = 1 ˆ
ˆ (g − f)(1) = − 3 2
( )
g
f
(−2) = 1
25
ˆ (f + g)(x) =3x − 1
Domain: (−∞, ∞)
ˆ (fg)(x) =2x 2 − 3x − 2
Domain: (−∞, ∞)
ˆ (f − g)(x) =x +3
Domain: (−∞, ∞)
( )
f
ˆ
g
(x) = 2x+1
x−2
Domain: (−∞, 2) ∪ (2, ∞)
12. For f(x) =1− 4x and g(x) =2x − 1
ˆ (f + g)(x) =−2x
Domain: (−∞, ∞)
ˆ (fg)(x) =−8x 2 +6x − 1
Domain: (−∞, ∞)
ˆ (f − g)(x) =2− 6x
Domain: (−∞, ∞)
( )
f
ˆ
g
(x) = 1−4x
2x−1
Domain: ( −∞, 1 ) (
2 ∪ 1
2 , ∞)