NAME ______________________________________________ DATE______________ PERIOD _____
7-1 7-1
Practice Operations on Functions
冢f冣
Find (f ⫹ g)(x), ( f ⫺ g)(x), ( f ⭈ g)(x), and ᎏᎏ (x) for each f(x) and g(x). g 2. f(x) ⫽ 8x2
3. f(x) ⫽ x2 ⫹ 7x ⫹ 12
1 x
g(x) ⫽ x ⫺ 3
g(x) ⫽ x2 ⫺ 9
g(x) ⫽ ᎏ2
Lesson 7-1
1. f(x) ⫽ 2x ⫹ 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For each set of ordered pairs, find f ⴰ g and g ⴰ 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)}
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)}
Find [ g ⴰ h](x) and [h ⴰ g](x). 8. g(x) ⫽ 3x h(x) ⫽ x ⫺ 4 11. g(x) ⫽ x ⫹ 3 h(x) ⫽ 2x2
9. g(x) ⫽ ⫺8x h(x) ⫽ 2x ⫹ 3 12. g(x) ⫽ ⫺2x h(x) ⫽ x2 ⫹ 3x ⫹ 2
10. g(x) ⫽ x ⫹ 6 h(x) ⫽ 3x2 13. g(x) ⫽ x ⫺ 2 h(x) ⫽ 3x2 ⫹ 1
If f(x) ⫽ x2, g(x) ⫽ 5x, and h(x) ⫽ x ⫹ 4, find each value. 14. f[ g(1)]
15. g[h(⫺2)]
16. h[f(4)]
17. f[h(⫺9)]
18. h[ g(⫺3)]
19. g[f(8)]
20. h[f(20)]
21. [f ⴰ (h ⴰ g)](⫺1)
22. [f ⴰ (g ⴰ h)](4)
23. 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. n
f
24. MEASUREMENT The formula f ⫽ ᎏᎏ converts inches n to feet f, and m ⫽ ᎏᎏ converts 12 5280 feet to miles m. Write a composition of functions that converts inches to miles.
Chapter 7
9
Glencoe Algebra 2
Chapter 7
冢 冣
Operations on Functions
Skills Practice
____________ PERIOD _____
x⫹5 ᎏᎏ , x ⫽ 4 x⫺4
⫹ x ⫺ 20; 3 2
g(x) ⫽ 2x ⫺ 3 ᎏᎏ, x ⫽ ᎏᎏ
3x ⫹ 1 2x ⫺ 3
2. f(x) ⫽ 3x ⫹ 1 5x ⫺ 2; x ⫹ 4; 6x 2 ⫺ 7x ⫺ 3;
x2
x2
3x2
A3
⫹ 5x ⫺ 5; h(x) ⫽ 2x2 ⫺ 3
Glencoe Algebra 2
Answers
8
Glencoe Algebra 2
23. [f ⴰ ( g ⴰ h)](⫺2) 21
22. [f ⴰ (h ⴰ g)](1) 72
21. f[h(8)] 189
Chapter 7
20. h[f(10)] 899
19. g[h(⫺3)] 12
18. h[f(5)] 224
17. g[f(⫺1)] 1
⫹ 8x ⫹ 5
16. g[h(0)] 3
⫺ 1; 2x 2
15. f[ g(1)] 15
If f(x) ⫽ 3x, g(x) ⫽ x ⫹ 4, and h(x) ⫽ x2 ⫺ 1, find each value.
h(x) ⫽ x2 ⫹ x ⫺ 1 25x 2 ⫹ 5x ⫺ 1
14. g(x) ⫽ x ⫹ 2 2x 2
12. g(x) ⫽ x ⫺ 3 x 2 ⫺ 3; x 2 ⫺ 6x ⫹ 9 h(x) ⫽ x2
11. g(x) ⫽ x ⫺ 6 x; x h(x) ⫽ x ⫹ 6
13. g(x) ⫽ 5x 5x 2
10. g(x) ⫽ ⫺3x ⫺12x ⫹ 3; ⫺12x ⫺ 1 h(x) ⫽ 4x ⫺ 1
{(⫺3, 6), (3, 6), (6, ⫺3)}; {(6, ⫺3), (⫺3, 6), (1, 6)}
8. f ⫽ {(6, 6), (⫺3, ⫺3), (1, 3)} g ⫽ {(⫺3, 6), (3, 6), (6, ⫺3)}
{(⫺3, 2), (2, ⫺3)}; {(0, 1), (1, 0), (2, 0)}
6. f ⫽ {(0, ⫺3), (1, 2), (2, 2)} g ⫽ {(⫺3, 1), (2, 0)}
9. g(x) ⫽ 2x 2x ⫹ 4; 2x ⫹ 2 h(x) ⫽ x ⫹ 2
Find [g ⴰ h](x) and [h ⴰ g](x).
{(1, 3), (2, 1), (3, 1)}; {(⫺4, ⫺1), (⫺1, ⫺4), (2, ⫺1)}
7. f ⫽ {(⫺4, 3), (⫺1, 1), (2, 2)} g ⫽ {(1, ⫺4), (2, ⫺1), (3, ⫺1)}
{(0, ⫺2), (⫺2, 0), (5, 0)}; {(0, 4), (4, 0)}
5. f ⫽ {(0, 0), (4, ⫺2)} g ⫽ {(0, 4), (⫺2, 0), (5, 0)}
For each set of ordered pairs, find f ⴰ g and g ⴰ f if they exist.
x2
3x3 ⫹ 5 3x3 ⫺ 5 ᎏᎏ, x ⫽ 0; ᎏᎏ, x ⫽ 0; 3. f(x) ⫽ ⫺ x ⫹ 4; ⫹ x ⫺ 4; 4. f(x) ⫽ x x 3 2 3x x 5 g(x) ⫽ 4 ⫺ x 4x 2 ⫺ x3; ᎏ , x ⫽ 4 g(x) ⫽ ᎏᎏ 15x, x ⫽ 0; ᎏᎏ, x ⫽ 0 x 5 4⫺x
g(x) ⫽ x ⫺ 4
x2
1. f(x) ⫽ x ⫹ 5 2x ⫹ 1; 9;
f Find (f ⫹ g)(x), (f ⫺ g)(x), (f ⭈ g)(x), and ᎏ (x) for each f(x) and g(x). g
7-1
NAME ______________________________________________ DATE
冢f冣
Operations on Functions
Practice
____________ PERIOD _____
8, x ⫽ 0; 8x 4, x ⫽ 0
⫹1 ᎏᎏ , x ⫽ 0; x2 4 8x ⫺ 1 ᎏᎏ , x ⫽ 0; x2
x⫹4 ᎏᎏ, x ⫽ ⫾3 x⫺3
x 4 ⫹ 7x 3 ⫹ 3x 2 ⫺ 63x ⫺ 108;
2x 2 ⫹ 7x ⫹ 3; 7x ⫹ 21;
g(x) ⫽ x2 ⫺ 9
3. f(x) ⫽ x2 ⫹ 7x ⫹ 12
⫺2x 2 ⫺ 6x ⫺ 4; 4x 2 ⫺ 6x ⫹ 2
12. g(x) ⫽ ⫺2x h(x) ⫽ x2 ⫹ 3x ⫹ 2
⫺16x ⫺ 24; ⫺16x ⫹ 3
9. g(x) ⫽ ⫺8x h(x) ⫽ 2x ⫹ 3
n
f
Chapter 7
[m ⴰ f ]n ⫽ ᎏᎏ
n 63,360
9
Glencoe Algebra 2
24. MEASUREMENT The formula f ⫽ ᎏᎏ converts inches n to feet f, and m ⫽ ᎏᎏ converts 12 5280 feet to miles m. Write a composition of functions that converts inches to miles.
C(x) ⫽ 1150 ⫺ 0.011x 2
22. [f ⴰ (g ⴰ h)](4) 1600 23. 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.
19. g[f(8)] 320 21. [f ⴰ (h ⴰ g)](⫺1) 1 20. h[f(20)] 404
16. h[f(4)] 20 18. h[ g(⫺3)] ⫺11
15. g[h(⫺2)] 10 17. f[h(⫺9)] 25
14. f[ g(1)] 25
3x 2 ⫺ 1; 3x 2 ⫺ 12x ⫹ 13
13. g(x) ⫽ x ⫺ 2 h(x) ⫽ 3x2 ⫹ 1
3x 2 ⫹ 36x ⫹ 108
10. g(x) ⫽ x ⫹ 6 h(x) ⫽ 3x2 3x 2 ⫹ 6;
does not exist; {(0, 0), (1, 0), (6, 2)}
7. f ⫽ {(0, ⫺3), (1, ⫺3), (6, 8)} g ⫽ {(8, 2), (⫺3, 0), (⫺3, 1)}
{(⫺2, ⫺2), (3, ⫺2)}; {(⫺4, 1), (0, 0), (1, 0)}
5. f ⫽ {(⫺4, 3), (0, ⫺2), (1, ⫺2)} g ⫽ {(⫺2, 0), (3, 1)}
If f(x) ⫽ x2, g(x) ⫽ 5x, and h(x) ⫽ x ⫹ 4, find each value.
2x 2 ⫹ 3; 2x 2 ⫹ 12x ⫹ 18
11. g(x) ⫽ x ⫹ 3 h(x) ⫽ 2x2
3x ⫺ 12; 3x ⫺ 4
8. g(x) ⫽ 3x h(x) ⫽ x ⫺ 4
Find [g ⴰ h](x) and [h ⴰ g](x).
{(6, 6), (⫺5, 3), (3, ⫺5)}; {(⫺4, 0), (0, ⫺4), (1, 1)}
6. f ⫽ {(⫺4, ⫺5), (0, 3), (1, 6)} g ⫽ {(6, 1), (⫺5, 0), (3, ⫺4)}
{(0, ⫺1), (⫺1, 4), (4, 0)}; {(⫺9, 3), (⫺1, ⫺9), (3, ⫺1)}
4. f ⫽ {(⫺9, ⫺1), (⫺1, 0), (3, 4)} g ⫽ {(0, ⫺9), (⫺1, 3), (4, ⫺1)}
For each set of ordered pairs, find f ⴰ g and g ⴰ f if they exist.
2x ⫹ 1 ᎏᎏ, x ⫽ 3 x⫺3
2x 2 ⫺ 5x ⫺ 3;
3x ⫺ 2; x ⫹ 4;
g(x) ⫽ ᎏ2
g(x) ⫽ x ⫺ 3
8x 4
2. f(x) ⫽ 8x2
1. f(x) ⫽ 2x ⫹ 1 1 x
Find (f ⫹ g)(x), (f ⫺ g)(x), (f ⭈ g)(x), and ᎏᎏ (x) for each f(x) and g(x). g
7-1 7-1
NAME ______________________________________________ DATE
Answers (Lesson 7-1)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
