c and Those complex num black, while those that lead to un used similar ideas to generate his own recurs The image "i of the storm" reproduced here function the is based f(2) = (1-i)z*+(7+1)z where again z is a 2z +6 %3D variable that will be replaced with complex numbers. The image is actually a picture of the complex plane, with the origin in the very center of the golden ring. The golden ring consists of those complex numbers that lie a distance between 0.9 and 1.1 units from the origin. The rules for coloring other complex numbers in the plane are as follows: given an initial complex number z not on the gold ring, f(z) is calculated. If the complex number f(z) lies somewhere on the gold ring, the original number z is colored the deepest shade of green. If not, the iterate f (z) is calculated. If this result lies in the gold ring, the original z is colored a bluish shade of green. If not, the process continues up to the 12th iterate f (z), using a different color time. If f" (z) lies in the gold ring, z is colored red, and if not the process halts and z is colored black. The idea of recursion can be used to generate any number of similar images, with the end result usually striking and often surprising even to the creator. Exercises In each of the following problems, use the information given to determine a. (f + g)(-1). f b. (f -g)(-1),c. (fg)(-1), and d. (4) -(-1). See Examples 1,2, and 3. 1. f(-1)=-3 and g(-1)=5 2. f(-1)=0 and g(-1)=-1 3. f(x)=x² – 3 and g(x)= x %3D 4. f(x)= Vx and g(x)= x – 1 5. f(-1)= 15 and g(-1)=-3 6. f(x)= and g(x)= 6x %3D %3D 7. f(x)=x* +1 and g(x) = x" +2 %3D 8. f(x)=, 6-X and g(x) = %3D 9. f={(5, 2).(0, – 1).(-1, 3).(-2, 4)} and g = {(-1, 3).(0, 5)} -4 %3D 10. f = {(3,15).(2, – 1).(-1, 1)} and g(x)= -2 283 Combining Functions Section 3.6 11. 12. 4. 4 2 -2 -2 -4 -4 -4 -2 0 2 4 -4 -2 2 4 13. 14. 4 4 0+ 0+ -2 -2 -4 -4 -4 -2 0 -4 -2 4 In each of the following problems, find a. the formula and domain for f+ g, and b. the formula and domain for See Examples 2 and 3. 15. f(x)=|x| and g (x) = Vx 16. f(x) = x² -1 and g(x)= {x %3D 3 17. f(x)=x-1 and g(x) = x² – 1 18. f(x)= x² and g (x)= x – 3 19. f(x) = 3x and g(x)= x' –8 20. f(x) = x² +4 and g (x) = /x – 2 2 21. f(x)=-2x² and g(x)=|x+4| 22. f (x)= 6x – 1 and g (x) = x³ 4- ఉం 2. 2. 2.

Question

I need questions 12,13,17,20

c and
Those complex num
black, while those that lead to un
used similar ideas to generate his own recurs
The image "i of the storm" reproduced
here
function
the
is
based
f(2) = (1-i)z*+(7+1)z where again z is a
2z +6
%3D
variable that will be replaced with complex
numbers. The image is actually a picture of
the complex plane, with the origin in the
very center of the golden ring. The golden
ring consists of those complex numbers
that lie a distance between 0.9 and 1.1 units
from the origin. The rules for coloring
other complex numbers in the plane are as
follows: given an initial complex number z
not on the gold ring, f(z) is calculated. If
the complex number f(z) lies somewhere on the gold ring, the original number z is
colored the deepest shade of green. If not, the iterate f (z) is calculated.
If this result lies in the gold ring, the original z is colored a bluish shade of green. If
not, the process continues up to the 12th iterate f (z), using a different color
time. If f" (z) lies in the gold ring, z is colored red, and if not the process halts and z
is colored black.
The idea of recursion can be used to generate any number of similar images, with the
end result usually striking and often surprising even to the creator.
Exercises
In each of the following problems, use the information given to determine a. (f + g)(-1).
f
b. (f -g)(-1),c. (fg)(-1), and d.
(4)
-(-1). See Examples 1,2, and 3.
1. f(-1)=-3 and g(-1)=5
2. f(-1)=0 and g(-1)=-1
3. f(x)=x² – 3 and g(x)= x
%3D
4. f(x)= Vx and g(x)= x – 1
5. f(-1)= 15 and g(-1)=-3
6. f(x)=
and g(x)= 6x
%3D
%3D
7. f(x)=x* +1 and g(x) = x" +2
%3D
8. f(x)=,
6-X
and g(x) =
%3D
9. f={(5, 2).(0, – 1).(-1, 3).(-2, 4)} and g = {(-1, 3).(0, 5)}
-4
%3D
10. f = {(3,15).(2, – 1).(-1, 1)} and g(x)= -2
View transcribed image text
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283
Combining Functions Section 3.6
11.
12.
4.
4
2
-2
-2
-4
-4
-4
-2 0
2
4
-4
-2
2 4
13.
14.
4
4
0+
0+
-2
-2
-4
-4
-4
-2 0
-4
-2
4
In each of the following problems, find a. the formula and domain for f+ g, and b. the
formula and domain for
See Examples 2 and 3.
15. f(x)=|x| and g (x) = Vx
16. f(x) = x² -1 and g(x)= {x
%3D
3
17. f(x)=x-1 and g(x) = x² – 1
18. f(x)= x² and g (x)= x – 3
19. f(x) = 3x and g(x)= x' –8
20. f(x) = x² +4 and g (x) = /x – 2
2
21. f(x)=-2x² and g(x)=|x+4|
22. f (x)= 6x – 1 and g (x) = x³
4-
ఉం
2.
2.
2.
View transcribed image text
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Transcribed Image Text

c and Those complex num black, while those that lead to un used similar ideas to generate his own recurs The image "i of the storm" reproduced here function the is based f(2) = (1-i)z*+(7+1)z where again z is a 2z +6 %3D variable that will be replaced with complex numbers. The image is actually a picture of the complex plane, with the origin in the very center of the golden ring. The golden ring consists of those complex numbers that lie a distance between 0.9 and 1.1 units from the origin. The rules for coloring other complex numbers in the plane are as follows: given an initial complex number z not on the gold ring, f(z) is calculated. If the complex number f(z) lies somewhere on the gold ring, the original number z is colored the deepest shade of green. If not, the iterate f (z) is calculated. If this result lies in the gold ring, the original z is colored a bluish shade of green. If not, the process continues up to the 12th iterate f (z), using a different color time. If f" (z) lies in the gold ring, z is colored red, and if not the process halts and z is colored black. The idea of recursion can be used to generate any number of similar images, with the end result usually striking and often surprising even to the creator. Exercises In each of the following problems, use the information given to determine a. (f + g)(-1). f b. (f -g)(-1),c. (fg)(-1), and d. (4) -(-1). See Examples 1,2, and 3. 1. f(-1)=-3 and g(-1)=5 2. f(-1)=0 and g(-1)=-1 3. f(x)=x² – 3 and g(x)= x %3D 4. f(x)= Vx and g(x)= x – 1 5. f(-1)= 15 and g(-1)=-3 6. f(x)= and g(x)= 6x %3D %3D 7. f(x)=x* +1 and g(x) = x" +2 %3D 8. f(x)=, 6-X and g(x) = %3D 9. f={(5, 2).(0, – 1).(-1, 3).(-2, 4)} and g = {(-1, 3).(0, 5)} -4 %3D 10. f = {(3,15).(2, – 1).(-1, 1)} and g(x)= -2

283 Combining Functions Section 3.6 11. 12. 4. 4 2 -2 -2 -4 -4 -4 -2 0 2 4 -4 -2 2 4 13. 14. 4 4 0+ 0+ -2 -2 -4 -4 -4 -2 0 -4 -2 4 In each of the following problems, find a. the formula and domain for f+ g, and b. the formula and domain for See Examples 2 and 3. 15. f(x)=|x| and g (x) = Vx 16. f(x) = x² -1 and g(x)= {x %3D 3 17. f(x)=x-1 and g(x) = x² – 1 18. f(x)= x² and g (x)= x – 3 19. f(x) = 3x and g(x)= x' –8 20. f(x) = x² +4 and g (x) = /x – 2 2 21. f(x)=-2x² and g(x)=|x+4| 22. f (x)= 6x – 1 and g (x) = x³ 4- ఉం 2. 2. 2.