College Algebra, 2013a

1.5 Function Arithmetic 87
1.5.2 Answers
1. For f(x) =3x + 1 and g(x) =4− x
ˆ (f + g)(2) = 9 ˆ (f − g)(−1) = −7 ˆ (g − f)(1) = −1
ˆ (fg) ( ) ( )
( )
1
2 =
35
f
4 ˆ
g
(0) = 1 g
4
ˆ
f
(−2) = − 6 5
2. For f(x) =x 2 and g(x) =−2x +1
ˆ (f + g)(2) = 1 ˆ (f − g)(−1) = −2 ˆ (g − f)(1) = −2
ˆ (fg) ( ( )
( )
1
2)
=0
f
ˆ
g
(0) = 0 g
ˆ
f
(−2) = 5 4
3. For f(x) =x 2 − x and g(x) =12− x 2
ˆ (f + g)(2) = 10 ˆ (f − g)(−1) = −9 ˆ (g − f)(1) = 11
ˆ (fg) ( ) ( )
( )
1
2 = −
47
f
16 ˆ
g
(0) = 0 g
ˆ
f
(−2) = 4 3
4. For f(x) =2x 3 and g(x) =−x 2 − 2x − 3
ˆ (f + g)(2) = 5 ˆ (f − g)(−1) = 0 ˆ (g − f)(1) = −8
ˆ (fg) ( ) ( )
( )
1
2 = −
17
f
16 ˆ
g
(0) = 0 g
ˆ
f
(−2) = 3
16
5. For f(x) = √ x + 3 and g(x) =2x − 1
ˆ (f + g)(2) = 3 + √ 5 ˆ (f − g)(−1) = 3 + √ 2 ˆ (g − f)(1) = −1
ˆ (fg) ( ( )
1
2)
=0
f
ˆ
g
(0) = − √ ( )
3 g
ˆ
f
(−2) = −5
6. For f(x) = √ 4 − x and g(x) = √ x +2
ˆ (f + g)(2) = 2 + √ 2 ˆ (f − g)(−1) = −1+ √ 5 ˆ (g − f)(1) = 0
ˆ (fg) ( ) √ ( )
1
2 = 35
f
2 ˆ
g
(0) = √ ( )
2 g
ˆ
f
(−2) = 0