College Algebra, 2013a

1.4 Function Notation 71
18. For f(x) =0
ˆ f(3) = 0 ˆ f(−1) = 0 ˆ f ( 3
2)
=0
ˆ f(4x) =0 ˆ 4f(x) =0 ˆ f(−x) =0
ˆ f(x − 4) = 0 ˆ f(x) − 4=−4 ˆ f ( x 2) =0
19. For f(x) =2x − 5
ˆ f(2) = −1 ˆ f(−2) = −9 ˆ f(2a) =4a − 5
ˆ 2f(a) =4a − 10 ˆ f(a +2)=2a − 1 ˆ f(a)+f(2) = 2a − 6
ˆ f ( )
2
a =
4
a − 5
= 4−5a
a
ˆ f(a)
2
= 2a−5
2
ˆ f(a + h) =2a +2h − 5
20. For f(x) =5− 2x
ˆ f(2) = 1 ˆ f(−2) = 9 ˆ f(2a) =5− 4a
ˆ 2f(a) =10− 4a ˆ f(a +2)=1− 2a ˆ f(a)+f(2) = 6 − 2a
ˆ f ( )
2
a =5−
4
a
= 5a−4
a
ˆ f(a)
2
= 5−2a
2
ˆ f(a + h) =5− 2a − 2h
21. For f(x) =2x 2 − 1
ˆ f(2) = 7 ˆ f(−2) = 7 ˆ f(2a) =8a 2 − 1
ˆ 2f(a) =4a 2 − 2 ˆ f(a +2)=2a 2 +8a +7 ˆ f(a)+f(2) = 2a 2 +6
ˆ f ( )
2
a =
8
− 1
a 2
= 8−a2
a 2
ˆ f(a)
2
= 2a2 −1
2
ˆ f(a + h) =2a 2 +4ah +
2h 2 − 1