Composite Functions, please confirm

[dylanjames]

New to composite functions here. Lesson has been vague and unhelpful.. again. Here is what I've worked on so far but not sure on the last equation in particular, or that I have done my multiplication properly when working with a squared set of brackets, multiplied by an number.. (b and c)
Any confirmation/help would be mucho appreciated. Thanks!

Given the functions f(x)=4x-1, g(x)=3-2^2 and h(x)=√(x+5) simplify the following..

a) f(g(a))
g(a)=4(3-2a^2) - 1
=12 - 8a^2 - 1
=11-8a^2.

b) g(f(2x))
f(2x)=4(2x)-1=8x-1
g(f(2x)=3-2(8x-1)^2
g(f(2x)=3-2[(8x-1)(8x-1)]
g(f(2x))=3-2[64x^2 -16x+1]
g(f(2x)=-128x^2+32x-2+3
g(f(2x)=-128x^2+32x+1

c) h(g(2k+1))
g(2k+1)=3-2(2k+1)^2
=3-2[(2k+1)(2k+1)]
=3-2[4k^2 +4k+1]
=-8k^2-8k+1
h(g(2k+1))=sqrt[(-8k^2-8k+1)+5] =?
=-8k-2.82k+2.23? = 10.82k+2.23...
That can't be right...

Also need the domain and range for f(g(x))... no idea how to tackle that.

 

[SammyS]

New to composite functions here. Lesson has been vague and unhelpful.. again. Here is what I've worked on so far but not sure on the last equation in particular, or that I have done my multiplication properly when working with a squared set of brackets, multiplied by an number.. (b and c)
Any confirmation/help would be mucho appreciated. Thanks!

Given the functions f(x)=4x-1, g(x)=3-2x^2 and h(x)=√(x+5) simplify the following..
There's a typo in g(x).

a) f(g(a))
g(a)=4(3-2a^2) - 1
=12 - 8a^2 - 1
=11-8a^2.

b) g(f(2x))
f(2x)=4(2x)-1=8x-1
g(f(2x)=3-2(8x-1)^2
g(f(2x)=3-2[(8x-1)(8x-1)]
g(f(2x))=3-2[64x^2 -16x+1]
g(f(2x)=-128x^2+32x-2+3
g(f(2x)=-128x^2+32x+1

c) h(g(2k+1))
g(2k+1)=3-2(2k+1)^2
=3-2[(2k+1)(2k+1)]
=3-2[4k^2 +4k+1]
=-8k^2-8k+1
h(g(2k+1))=sqrt[(-8k^2-8k+1)+5] =?
=-8k-2.82k+2.23? = 10.82k+2.23...
That can't be right...

Also need the domain and range for f(g(x))... no idea how to tackle that.

$\displaystyle\ h(g(2k+1))=\sqrt{-8k^2-8k+1+5\ }$ is correct.

You can't split up the square root like that.

$\displaystyle\ \sqrt{a+b}\ne\sqrt{a}+\sqrt{b}$​

 

[Mark44]

@dylanjames, when you post a problem, don't delete the homework template.

 

[dylanjames]

So how do I solve the domain of that function?

 

[SammyS]

So how do I solve the domain of that function?

What is meant by the implicit domain of a function, or meant by determining the domain of a function implicitly?

 

[dylanjames]

English dude!

 

[SammyS]

English dude!

What sort of math class is this?

What is meant by the domain of a function anyway ?

 

[dylanjames]

An extremely poorly taught advanced functions class, that throws its students two small examples, slams them with 35 homework questions that go 6 steps further than taught and do me no good in terms of actually understanding material. I have solved the question. Thank you.

 

[Mark44]

What is meant by the implicit domain of a function, or meant by determining the domain of a function implicitly?

English dude!

What Sammy wrote was English. Chill on the attitude, dude, and show some respect, or else...

 

[dylanjames]

Relax mark. Little bit of sarcasm got your knickers in a twist?

 

[Mark44]

Relax mark. Little bit of sarcasm got your knickers in a twist?

Sarcasm often doesn't come off well in a social media environment. In post #5 Sammy tried to get you to think about your question, and you replied with a flippant "English dude!" Whether you realize it or not, he was trying to help you. When he asked what type of class you were in, in post 7, I don't believe he was primarily interested in your opinion of how the class was run, but instead what the level of the class was.

You're the one asking for help. Sammy and others are helping completely voluntarily, so show some respect for those who are trying to help you understand this stuff. The "or else" means that this is your warning. There won't be others.

 

[dylanjames]

Lighten up. No disrespect to Sammy intended but I do believe this is why people have such a terrible perception of math-oriented people, and professors too for that matter.
Life is too short to sweat the little things Mark and ill be damned if I am going to sit on here and be lectured by some retired math professor, eager to relive his years as the "the man in charge" to compensate for his little man complex. Does it matter in the grand scheme of things whether each of the homework threads are posted in your perfect little columns? No. Does it make any difference that you send out lord knows how many emails to people complaining about their accidentally misplaced forums?? No.
Furthermore, does it matter that you are going to ban me from a forum that I can join in again under a new name in approximately 12 seconds?!?

Lighten up man. When the dust settles, you know I'm right. Cheers.

 

[Mark44]

Lighten up. No disrespect to Sammy intended but I do believe this is why people have such a terrible perception of math-oriented people, and professors too for that matter.
Life is too short to sweat the little things Mark and ill be damned if I am going to sit on here and be lectured by some retired math professor, eager to relive his years as the "the man in charge" to compensate for his little man complex. Does it matter in the grand scheme of things whether each of the homework threads are posted in your perfect little columns?

If you post a homework question, you need to use the template. Them's the rules. See https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/, second bullet under Homework Guidelines.

Attempts are mandatory
You MUST show that you have attempted to answer your question in order to receive help. You MUST make use of the homework template, which automatically appears when a new topic is created in the homework help forums.

You agreed to abide by these rules when you opened an account here. If you choose not to abide by them, your stay here will be short.

No. Does it make any difference that you send out lord knows how many emails to people complaining about their accidentally misplaced forums?? No.
Furthermore, does it matter that you are going to ban me from a forum that I can join in again under a new name in approximately 12 seconds?!?

You must think that no one has ever thought of this before. Just to set you straight, there have been a lot of members who were banned, and who signed up again with new user names. They didn't last long either.

Lighten up man. When the dust settles, you know I'm right. Cheers.

 

[Raghav Gupta]

Furthermore, does it matter that you are going to ban me from a forum that I can join in again under a new name in approximately 12 seconds?!?

It would not be beneficial to you, even if you sign up as a new user. You will get good responses to your questions only when you change to a good attitude and give respect.

You must know that some privileged members of PF can locate you by your IP address.
So changing up to a new user will not help you.