Question

Please help! Will fan and medal!

Question in comments!

Answer 1

@DannyO19

Answer 2

You must identify Domain restrictions. Look around f(x). Any restrictions. Look around g(x). Any restrictions.

Don't tag people with no work of your own showing.

Answer 3

I don't know what to do. I'm learning a little more each time I'm helped but as of right now I don't know where to even start on this problem. Don't be rude.

Answer 4

I'm never rude. Honesty and Directness are often mistaken for rudeness.

Take a good hard look at f(x). What value(s) for x might be a problem?

Answer 5

Well I apologize but that sounded rather sharp to me. And I don't know. I have no clue at all

Answer 6

I do not believe that.

Try x = 2. Any problem with that? 1/2 = 1/2 That seems fine.

Try x = -1. Any problem with that? 1/(-1) = -1. That seems fine.

Find something that doesn't seem fine.

Answer 7

0?

Answer 8

See!!! You DO have a clue. x = 0 is NOT in the Domain of f(x).

g(x) is a simple polynomial, so there are no restrictions, there.

f(g(x)) is a different story. We know f(x) can't have x = 0. What happens if g(x) = 0?

Answer 9

Uhm. it's iincorrect? I'm not sure. my lesson didn''t explain what you're talking about

Answer 10

We're talking about Domain. This has nothing to do with correct or incorrect.

f(x) cannot take x = 0. We established this.

f(g(x)) has exactly the same problem if g(x) = 0.

This needs to make sense.

f(fred) has a problem if fred = 0

f($%^) has a problem if $%^ = 0

Answer 11

Okay. so it's 0,_ how do we figure out the _?

Answer 12

I might be helping multiple students at the same time.

That's the spirit. Follow this logical path...

1) x = 0 is NOT in the Domain of f(x)
2) g(x) BETTER NOT be zero (0), if we wish to construct f(g(x)).
3) Where is g(x) = 0 so we can avoid that?

Answer 13

Yes?? o.o

Answer 14

Answer the question in #3, above.

Answer 15

I don't understand question 3 ._.

Answer 16

I think you need to do
(fog)(x) first.
Then look for domain restrictions.

Answer 17

No, that is not the way to proceed. Just answer the question in #3, above.

Constructing f(g(x)) may mask restrictions on the individual functions.

Answer 18

You don't understand where is g(x) = 0?

Answer 19

no. I don't really understand any of this. I don;t even know what a domain is.

Answer 20

Domain -- Values that can go in.

Have you ever seen such a problem as this: \(Solve\;for\;x: x^{2} - 6x = 0\)

Answer 21

Not except for the ones in previous questions I don't think so

Answer 22

Can you solve that one? It requires factoring.

Answer 23

I would need the steps honestly ._.

Answer 24

It seems we are at an impasse. You seem to be in the wrong class. The best I can do is suggest that you have a very sincere talk with your academic advisor. You don't seem to have the background for the class you are in. There should have been prerequisite requirements. :-(

Answer 25

They won't change them, these are the last two math classes and by the most stupid laws I HAVE to take these classes even though I have NO clue what the problems even ask half the time and I just want to be done.

Answer 26

Sadly, I thought you would say something like that. What to do... What to do...

We can't do two semester's worth of algebra on here in a week or so. What are your prospects for finding a local tutor? It would help A LOT to have someone sitting there, actually interacting with you. It can be very discouraging without faces.

Answer 27

@tkhunny Thanks for the explanation above.

Answer 28

I've tried. My school offers an old couple on an rv that drive around but they couldn't help me the last 3 times I went and I left more confused than when I went in. Other than that the only tutors around here are strictly for college or public school kids. I got help with spanish through OS but it's my last option. I'm already making as many meeting with teachers as I can but I still need the lessons done quicker or I won't graduate. OS is kind of my last option.

Answer 29

Well, you MUST get the necessary background. One place to look is PurpleMath. Another good one is KahnAcademy. If nothing else, when you encounter an unfamiliar term, such as "Domain", you can go look it up and see a useful discussion. Many online resources still have a lot to learn. These two sites seem to have a clue.

Answer 30

I tried Sal Kahn. His videos were never set up for the problems I was working and I'd just cry harder. And does that mean you don;t be helping me finish this question or are you helping another? :/

Answer 31

"Domain" is the key word here, and I agree fully with tkhunny that you need to understand this concept before the rest of the problem will make any sense.

Have you heard of or read of "composite functions?"

That's another concept important to understand before you try to solve this problem.

Answer 32

No :/ I've heard of them; don't remember them

Answer 33

What is your primary source for learning new concepts in your current math course? Have you a textbook? Do you have access to online learning materials (explanations)? Are you able to look up unfamiliar concepts on the Internet?

Answer 34

I have a tutorial online but it doesn't make sense to me. :/

Answer 35

If none of that, and none of what tkhunny and I are discussing makes sense to you, then you most likely are in the wrong class. Unfortunately, you may have to find a way to acquire more background knowledge and experience before you'll be able to cope with "domain," "composite functions" and the like.

When is this assignment due?

Can you afford (or can your parents afford) private tutoring locally, assuming that you could find someone qualified?

Answer 36

Have you actually looked up "domain of a function" on the 'Net?

Answer 37

Is there anyway we could just finish these last 3 questions for the night and I'll call my school tomorrow again? and it's over due. And no, we aren't exactly financially stable to start with. And the net didn't help I always check it first.

Answer 38

And my being in the wrong class or not my school will not give me some alternate thing I've begged them to but bacause of some stupid law I'm screwed.

Answer 39

Those are pretty tough constraints within to work. My take is that you DO have the potential to undrstand this material, but will have to find resources (human and online and in books) through which to acquire the necessary background knowledge and skills. what state are you in? are you home schooled? Do you ever attend classes? what's the reason for your having to learn this material online?

Answer 40

What's the very worst that could happen if you did not finish those last 3 questions?

Answer 41

Home school, ohio they do not offer classes the best I get is an online meeting which helps but not enough as the teachers are busy with other students. I only have 2 math credits to get my diploma but a previous school computer of mine was stolen so now I have a $700+fee before my transcripts will be released. And if I get 8/20 I'll pass the lesson assignment this is question 7. if I miss any more than two I fail and have to start all over again,. If you want to be technical I did 3 questions from this assignment before with Rhonda but got kicked when my internet went out and I had to restart again otherwise I'd be done with this lesson

Answer 42

Perhaps you should investigate going to a bricks-and-mortar public school, if this home schooling and online learning isn't working well for you.

I'm going to do an experiement.

I'm giving you the function f(x) = 1/x, which is called "the reciprocal of x."
x is the independent variable. With one important exception, you can choose any number you want for x. What is that one exc eption?

Answer 43

My school won't release my transcripts and no brick and mortar school will take me for two math credits. and the exception is 0?

Answer 44

Yes, the exception is 0. We'd say, "0 is not part of the domain of f(x) = 1/x."
Any other input would be acceptable. Thus, the domain of this function is

(-inf, 0) U (0, inf). which can be intepreted: all negative numbers less than zero and also all positive numbers greater than zero.

Answer 45

f(x)=1/x. Suppose that x=5. Find f(5).

Answer 46

-5?

Answer 47

No negative. You were correct before when you said 0 is not part of the domain of f(x). f(0) would be 1/0. what's wrong with that?

Answer 48

It would equal 0

Answer 49

Note how x takes on the value 0 on the left of this equation, and x on the right also takes on that same value, 0.

f(1)=1/(1) = ? is 1 in the domain of f(x)?

1/0 is not equal to 0. In fact, it's not even defined. We'd say, "division by zero is undefined." That's why 0 is NOT part of the domain of f(x)=1/x.

Answer 50

what is f(2), for the same function?

Answer 51

I'm not sure...

Answer 52

What I've been trying to do is to test your knowledge of essential prerequisites for successfully completing the problem at hand. Sad to say, it's obvious you're having difficulty.

Division by zero is undefined... so 1/0 has NO numerical answer.

f(1) is found by replacing x in 1/x with 1; the result looks like 1/1 and has the value 1.

f(2) is found by replacing x in 1/x with 2. What's the result?

Answer 53

1/2

Answer 54

Right. What's f(-3)?

Answer 55

that says, "What's the value of the function f when x equals negative 3?"

Answer 56

1/-3

Answer 57

Do exactly what you did before. to evaluate f(1), replace the x in f(x) = 1/x with 1. What's the result?

To evaluate f(-3), replace both x's in f(x) = 1/x with -3.

Answer 58

Right. Now suppose x=2c. Please enclose that within brackets: [2c]. What is f([2c])?

Review what you did before.

Answer 59

f(-3)=1/-3

Answer 60

That's correct for x = -3. Good.

But I'd already gone on to a new question. What if x = [2c]? find f( [2c] ). Follow exactly the same pattern as you did for x=-3.

Answer 61

Leave the brackes around the 2c: [2c].

Answer 62

f( [2c] ) = ?

Answer 63

f( [2c] ) =1/[2c]

Answer 64

so what 2 is the answer?

Answer 65

Perfect. You're doing fine, by following an established pattern.

The answer to my previous question is simply 1 / [2c].

Now find f ( g(x) ). Follow exactly the same pattern.

Answer 66

that says: Evaluate function f when its input is function g(x).

Answer 67

Whic values are we using for the variables here?

Answer 68

None! It's the concept of evaluating a function for any valid input that 's important.

Answer 69

My name is warren. Therefore, f(warren) is 1 / (warren).

Silly example, but it's exactly right and very relevant.

Answer 70

Evaluate f ( q(x) ). follow exactly the same pattern as before, and do not worry about numeric values; they're not needed.

Answer 71

@whateven?

Answer 72

I imagine this is tiring and perhaps discouraging for you. But through practice these patterns and definitions will become clearer.

Answer 73

f(q(x))=1/(q(x))

Answer 74

Great. Now, back to our original question. You were given f(x) = 1/x and g(x) = x^2-6x.

Can you now evaluate f(x) with the input x^2-6? Be sure to enclose that x^2-6x within parentheses.

Answer 75

Follow exactly the same pattern as before.

Answer 76

f(x^2-2)=1/(x^2-2)

Answer 77

that's correct, down to the last detail. Good.

Answer 78

Once more. Same f(x), but suppose g(x) = x^2 - 6x. First enclose x^2 - 6x in parentheses. Then, find

f( (x^2 - 6x).

Answer 79

f(g(x)=f(1/(x^2-6)

Answer 80

One "x" is missing there. Also, you don't need and should not write "f" in the right side.

we didn't write f on the right side before.

f(x)=1/x, g(x) = x^2 - 6x. Enclose x^2 - 6x) within parentheses first and then find

f( g(x)), where g(x) = (x^2 - 6x).

Answer 81

Same pattern as before. f(x) = 1/x

Answer 82

@whateven? Do you need a break?

Answer 83

I just got a notification that I have ten minutes left or I get kicked from my assignment. And no I need this to be done so I don't have to look at it anymore If I stop now I have to start from scratch and I'll be on one lesson for over a week

Answer 84

So, what are you planning to do now, and (if you had your way) what are you hoping to get from me?

I really cannot and will not hand out answers if we haven't established that you can find answers correctly yourself most of the time.

Answer 85

Yea I figured and I don't like asking for answers flat out but since it's either that or get kicked and have to start from scratch and you won't answer if I did ask anyway I'll just try and go to bed for the night...

Answer 86

To answer my own question, the function f(x) evaluated at g(x)=x^2-6x is