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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)
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)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@triciaal please help me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So this looks to be an excercise of dealing with functions. Functions can be added subtracted, multiplied, or divided much like numbers.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But crucially they can also be composed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For part (a) you need to add the two funtions a(x) + b(x)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444149834166:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0group like terms and simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for part a, it says to add (a+b)(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is the simplest example: a(x) + b(x) = (3x+10) + (2x8) = 5x +2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is a shorthand notation meant to say you are adding the functions to one another regardless of what the xvalue is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got that part but what about the x that needs to be multiplied to that solution of 5x + 2

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444149917064:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When dealing with functional notation the (x) is meant to refer to the argument of the function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0triciall, for part a what about the x that needs to be multiplied

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I can ignore the x for part a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It 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)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now what do you think part (b) should be?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444150022131:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0part c is a bit confusing

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0use b(x) as your x to find a(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which is called a composition

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0it is not confusing if you actually read the response

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A 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*58=108=2.... which means given x=5 b(5) gives 2

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444150296553:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then I have to do a(2)=3(2)+10=6+10=16

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now to execute this process abstractly (without reference to any particular x) we write the composition as a(b(x)) as triciaal has shown

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If 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))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does this make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03x+10 2x8 So if y=b(x)=2x8, Then a(y)=3y+10=3(2x8)+10=6x24+10=6x14=a(b(x))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Please let me know if this makes sense or if you are confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ChanelAnderson203 Do you understand? Would you like another example?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm still confused on C and sorry I was afk for a bit

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@triciaal I'm still confused on C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how are you confused on c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just don't understand what they mean if you could like start from the beginning of c that would be very helpful

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah let me go get my book

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444152446510:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444152528819:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0and then group like terms to simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so is 6x14 the answer for part c?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444152612850:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the full answer would be a{b(c)}=6x14

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh sorry ok thanks so much guys

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0who does the best response go to? :/ idk who xd

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks so much for your help guys :))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no problem have a good day

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0same goes for you @StudyWithMe!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and of course @triciaal too

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0thanks all the best to both of you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0see you some other time! :)
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