## anonymous one year ago HELP WILL FAN!!! l()()k<------------------------- Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (3 points) Part B: Find (a ⋅ b)(x). Show your work. (3 points) Part C: Find a[b(x)]. Show your work. (4 points)

1. anonymous

2. anonymous

Hello

3. anonymous

So this looks to be an excercise of dealing with functions. Functions can be added subtracted, multiplied, or divided much like numbers.

4. anonymous

yeah

5. anonymous

But crucially they can also be composed

6. anonymous

what do you mean

7. anonymous

For part (a) you need to add the two funtions a(x) + b(x)

8. triciaal

|dw:1444149834166:dw|

9. triciaal

group like terms and simplify

10. anonymous

for part a, it says to add (a+b)(x)

11. anonymous

This is the simplest example: a(x) + b(x) = (3x+10) + (2x-8) = 5x +2

12. anonymous

that is a shorthand notation meant to say you are adding the functions to one another regardless of what the x-value is

13. anonymous

I got that part but what about the x that needs to be multiplied to that solution of 5x + 2

14. triciaal

|dw:1444149917064:dw|

15. anonymous

When dealing with functional notation the (x) is meant to refer to the argument of the function

16. anonymous

triciall, for part a what about the x that needs to be multiplied

17. anonymous

so I can ignore the x for part a?

18. anonymous

It does not mean you are multiplying by the argument x... i.e. a(x) + b(x) can be writtedn (a+b)(x) or simply (a+b)

19. anonymous

Yes

20. anonymous

Now what do you think part (b) should be?

21. anonymous

Take a guess

22. triciaal

|dw:1444150022131:dw|

23. anonymous

part c is a bit confusing

24. triciaal

use b(x) as your x to find a(x)

25. anonymous

Which is called a composition

26. triciaal

it is not confusing if you actually read the response

27. anonymous

It wouldve been nice to try and have you work it out without knowing the answer first.... but the idea of a composition is that for a given x value you apply one function to it first.... then apply the second function to it

28. anonymous

A composition can be though of as just executing the functions in order 1 at a time... so given the value x=5 b(5)=2*5-8=10-8=2.... which means given x=5 b(5) gives 2

29. triciaal

|dw:1444150296553:dw|

30. anonymous

Then I have to do a(2)=3(2)+10=6+10=16

31. anonymous

Now to execute this process abstractly (without reference to any particular x) we write the composition as a(b(x)) as triciaal has shown

32. anonymous

If it helps you can think of it like this let y=b(x).... the composition of a and b (in this order) then means we are interested in a(y)=a(b(x))

33. anonymous

Does this make sense?

34. anonymous

3x+10 2x-8 So if y=b(x)=2x-8, Then a(y)=3y+10=3(2x-8)+10=6x-24+10=6x-14=a(b(x))

35. anonymous

Please let me know if this makes sense or if you are confused

36. anonymous

@ChanelAnderson203 Do you understand? Would you like another example?

37. anonymous

Well I have to go now hopefully this makes sense. Remember practice makes perfect and just like any language fluency in mathematics comes from learning all of the syntax and grammar as well as (unfortunately) all of the dialects that it contains. :D

38. anonymous

I'm still confused on C and sorry I was afk for a bit

39. anonymous

@triciaal I'm still confused on C

40. anonymous

for anyone here, I just need help with part c everything else I get please help its my last problem for my whole entire course pleasesss

41. anonymous

how are you confused on c

42. anonymous

I just don't understand what they mean if you could like start from the beginning of c that would be very helpful

43. anonymous

so can you help?

44. anonymous

yeah let me go get my book

45. anonymous

ok

46. anonymous

back

47. anonymous

kk

48. triciaal

|dw:1444152446510:dw|

49. anonymous

ok so far so good

50. triciaal

|dw:1444152528819:dw|

51. anonymous

3 (2x-8)+10

52. anonymous

6x-14??

53. triciaal

and then group like terms to simplify

54. anonymous

so is 6x-14 the answer for part c?

55. triciaal

|dw:1444152612850:dw|

56. anonymous

yes

57. anonymous

so the full answer would be a{b(c)}=6x-14

58. triciaal

not c x yes

59. anonymous

oh sorry ok thanks so much guys

60. anonymous

who does the best response go to? :/ idk who xd

61. triciaal

@StudyWithMe!

62. anonymous

do triciaal

63. anonymous

thanks so much for your help guys :))

64. triciaal

you are welcome

65. anonymous

no problem have a good day

66. anonymous

same goes for you @StudyWithMe!

67. anonymous

and of course @triciaal too

68. triciaal

thanks all the best to both of you

69. anonymous

see you some other time! :)