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NAME
6-1
DATE
PERIOD
Practice
Operations on Functions
(f)
Find ( f + g)(x), ( f - g)(x), ( f g)(x), and −
g (x) for each f(x) and g(x).
2. f(x) = 8x2
1. f(x) = 2x + 1
3. f(x) = x2 + 7x + 12
1
g(x) = −
2
g(x) = x - 3
g(x) = x2 - 9
x
3x - 2; x + 4;
2x 2 - 5x - 3;
2x + 1
x-3
−, x ≠ 3
8x 4 + 1
x
8x 4 - 1
−
, x ≠ 0;
x2
2x 2 + 7x + 3; 7x + 21;
−
, x ≠ 0;
2
x 4 + 7x 3 + 3x 2 - 63x - 108;
8, x ≠ 0; 8x 4, x ≠ 0
x+4
x-3
− , x ≠ ±3
For each pair of functions, find f ◦ g and g ◦ f , if they exist.
4. f = {(-9, -1), (-1, 0), (3, 4)}
g = {(0, -9), (-1, 3), (4, -1)}
5. f = {(-4, 3), (0, -2), (1, -2)}
g = {(-2, 0), (3, 1)}
{(0, -1), (-1, 4), (4, 0)};
{(-9, 3), (-1, -9), (3, -1)}
{(-2, -2), (3, -2)};
{(-4, 1), (0, 0), (1, 0)}
6. f = {(-4, -5), (0, 3), (1, 6)}
g = {(6, 1), (-5, 0), (3, -4)}
7. f = {(0, -3), (1, -3), (6, 8)}
g = {(8, 2), (-3, 0), (-3, 1)}
{(6, 6), (-5, 3), (3, -5)};
{(-4, 0), (0, -4), (1, 1)}
does not exist;
{(0, 0), (1, 0), (6, 2)}
8. g(x) = 3x
h(x) = x - 4
9. g(x) = -8x
h(x) = 2x + 3
3x - 12; 3x - 4
11. g(x) = x + 3
h(x) = 2x2
-16x - 24; -16x + 3
12. g(x) = -2x
h(x) = x2 + 3x + 2
2x 2 + 3;
2x 2 + 12x + 18
-2x 2 - 6x - 4;
4x 2 - 6x + 2
10. g(x) = x + 6
h(x) = 3x2
3x 2 + 6; 3x2 + 36x + 108
13. g(x) = x - 2
h(x) = 3x2 + 1
3x 2 - 1;
3x 2 - 12x + 13
If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value.
14. f[ g(1)] 25
15. g[h(-2)] 10
16. h[f(4)] 20
17. f [h(-9)] 25
18. h[ g(-3)] -11
19. g[ f(8)] 320
20. BUSINESS The function f(x) = 1000 - 0.01x2 models the manufacturing cost per item
when x items are produced, and g(x) = 150 - 0.001x2 models the service cost per item.
Write a function C(x) for the total manufacturing and service cost per item.
C(x) = 1150 - 0.011x 2
f
5280
n
converts inches n to feet f, and m = − converts
21. MEASUREMENT The formula f = −
12
feet to miles m. Write a composition of functions that converts inches to miles.
n
[m º f ](n) = −
63,360
Chapter 6
8
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find [ g ◦ h](x) and [h ◦ g](x), if they exist.