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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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)

Mathematics
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@triciaal please help me
Hello
So this looks to be an excercise of dealing with functions. Functions can be added subtracted, multiplied, or divided much like numbers.

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yeah
But crucially they can also be composed
what do you mean
For part (a) you need to add the two funtions a(x) + b(x)
|dw:1444149834166:dw|
group like terms and simplify
for part a, it says to add (a+b)(x)
This is the simplest example: a(x) + b(x) = (3x+10) + (2x-8) = 5x +2
that is a shorthand notation meant to say you are adding the functions to one another regardless of what the x-value is
I got that part but what about the x that needs to be multiplied to that solution of 5x + 2
|dw:1444149917064:dw|
When dealing with functional notation the (x) is meant to refer to the argument of the function
triciall, for part a what about the x that needs to be multiplied
so I can ignore the x for part a?
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)
Yes
Now what do you think part (b) should be?
Take a guess
|dw:1444150022131:dw|
part c is a bit confusing
use b(x) as your x to find a(x)
Which is called a composition
it is not confusing if you actually read the response
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
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
|dw:1444150296553:dw|
Then I have to do a(2)=3(2)+10=6+10=16
Now to execute this process abstractly (without reference to any particular x) we write the composition as a(b(x)) as triciaal has shown
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))
Does this make sense?
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))
Please let me know if this makes sense or if you are confused
@ChanelAnderson203 Do you understand? Would you like another example?
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
I'm still confused on C and sorry I was afk for a bit
@triciaal I'm still confused on C
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
how are you confused on c
I just don't understand what they mean if you could like start from the beginning of c that would be very helpful
so can you help?
yeah let me go get my book
ok
back
kk
|dw:1444152446510:dw|
ok so far so good
|dw:1444152528819:dw|
3 (2x-8)+10
6x-14??
and then group like terms to simplify
so is 6x-14 the answer for part c?
|dw:1444152612850:dw|
yes
so the full answer would be a{b(c)}=6x-14
not c x yes
oh sorry ok thanks so much guys
who does the best response go to? :/ idk who xd
do triciaal
thanks so much for your help guys :))
you are welcome
no problem have a good day
same goes for you @StudyWithMe!
and of course @triciaal too
thanks all the best to both of you
see you some other time! :)

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