anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@triciaal please help me
anonymous
  • anonymous
Hello
anonymous
  • anonymous
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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anonymous
  • anonymous
yeah
anonymous
  • anonymous
But crucially they can also be composed
anonymous
  • anonymous
what do you mean
anonymous
  • anonymous
For part (a) you need to add the two funtions a(x) + b(x)
triciaal
  • triciaal
|dw:1444149834166:dw|
triciaal
  • triciaal
group like terms and simplify
anonymous
  • anonymous
for part a, it says to add (a+b)(x)
anonymous
  • anonymous
This is the simplest example: a(x) + b(x) = (3x+10) + (2x-8) = 5x +2
anonymous
  • anonymous
that is a shorthand notation meant to say you are adding the functions to one another regardless of what the x-value is
anonymous
  • anonymous
I got that part but what about the x that needs to be multiplied to that solution of 5x + 2
triciaal
  • triciaal
|dw:1444149917064:dw|
anonymous
  • anonymous
When dealing with functional notation the (x) is meant to refer to the argument of the function
anonymous
  • anonymous
triciall, for part a what about the x that needs to be multiplied
anonymous
  • anonymous
so I can ignore the x for part a?
anonymous
  • 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)
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Now what do you think part (b) should be?
anonymous
  • anonymous
Take a guess
triciaal
  • triciaal
|dw:1444150022131:dw|
anonymous
  • anonymous
part c is a bit confusing
triciaal
  • triciaal
use b(x) as your x to find a(x)
anonymous
  • anonymous
Which is called a composition
triciaal
  • triciaal
it is not confusing if you actually read the response
anonymous
  • 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
anonymous
  • 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
triciaal
  • triciaal
|dw:1444150296553:dw|
anonymous
  • anonymous
Then I have to do a(2)=3(2)+10=6+10=16
anonymous
  • 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
anonymous
  • 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))
anonymous
  • anonymous
Does this make sense?
anonymous
  • 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))
anonymous
  • anonymous
Please let me know if this makes sense or if you are confused
anonymous
  • anonymous
@ChanelAnderson203 Do you understand? Would you like another example?
anonymous
  • 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
anonymous
  • anonymous
I'm still confused on C and sorry I was afk for a bit
anonymous
  • anonymous
@triciaal I'm still confused on C
anonymous
  • 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
anonymous
  • anonymous
how are you confused on c
anonymous
  • anonymous
I just don't understand what they mean if you could like start from the beginning of c that would be very helpful
anonymous
  • anonymous
so can you help?
anonymous
  • anonymous
yeah let me go get my book
anonymous
  • anonymous
ok
anonymous
  • anonymous
back
anonymous
  • anonymous
kk
triciaal
  • triciaal
|dw:1444152446510:dw|
anonymous
  • anonymous
ok so far so good
triciaal
  • triciaal
|dw:1444152528819:dw|
anonymous
  • anonymous
3 (2x-8)+10
anonymous
  • anonymous
6x-14??
triciaal
  • triciaal
and then group like terms to simplify
anonymous
  • anonymous
so is 6x-14 the answer for part c?
triciaal
  • triciaal
|dw:1444152612850:dw|
anonymous
  • anonymous
yes
anonymous
  • anonymous
so the full answer would be a{b(c)}=6x-14
triciaal
  • triciaal
not c x yes
anonymous
  • anonymous
oh sorry ok thanks so much guys
anonymous
  • anonymous
who does the best response go to? :/ idk who xd
triciaal
  • triciaal
@StudyWithMe!
anonymous
  • anonymous
do triciaal
anonymous
  • anonymous
thanks so much for your help guys :))
triciaal
  • triciaal
you are welcome
anonymous
  • anonymous
no problem have a good day
anonymous
  • anonymous
same goes for you @StudyWithMe!
anonymous
  • anonymous
and of course @triciaal too
triciaal
  • triciaal
thanks all the best to both of you
anonymous
  • anonymous
see you some other time! :)

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