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

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- anonymous

@triciaal please help me

- anonymous

Hello

- 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

yeah

- anonymous

But crucially they can also be composed

- anonymous

what do you mean

- anonymous

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

- triciaal

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- triciaal

group like terms and simplify

- anonymous

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

- anonymous

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

- 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

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

- triciaal

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- anonymous

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

- anonymous

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

- anonymous

so I can ignore the x for part a?

- 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

Yes

- anonymous

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

- anonymous

Take a guess

- triciaal

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- anonymous

part c is a bit confusing

- triciaal

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

- anonymous

Which is called a composition

- triciaal

it is not confusing if you actually read the response

- 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

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

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- anonymous

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

- 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

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

Does this make sense?

- 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

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

- anonymous

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

- 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

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

- anonymous

@triciaal I'm still confused on C

- 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

how are you confused on c

- 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

so can you help?

- anonymous

yeah let me go get my book

- anonymous

ok

- anonymous

back

- anonymous

kk

- triciaal

|dw:1444152446510:dw|

- anonymous

ok so far so good

- triciaal

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- anonymous

3 (2x-8)+10

- anonymous

6x-14??

- triciaal

and then group like terms to simplify

- anonymous

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

- triciaal

|dw:1444152612850:dw|

- anonymous

yes

- anonymous

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

- triciaal

not c x yes

- anonymous

oh sorry ok thanks so much guys

- anonymous

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

- triciaal

@StudyWithMe!

- anonymous

do triciaal

- anonymous

thanks so much for your help guys :))

- triciaal

you are welcome

- anonymous

no problem have a good day

- anonymous

same goes for you @StudyWithMe!

- anonymous

and of course @triciaal too

- triciaal

thanks all the best to both of you

- anonymous

see you some other time! :)

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