Finding the Domain of Composite Function

[Ebba Sen Pai]

Hello all. So my problem is this:

So I initially thought I had function domains down pretty well, but it seems I am lacking something important. I will try to explain my reasoning as follows:

"I can tell that for our function g(x), we must exclude all negative numbers as they will produce unhelpful imaginary numbers which don't belong in our domain.
Thus the domain of g(x) would read [0,infinity)
I can also tell that we must exclude any values of g(x) from that will produce a value of 3 in f(g(x)) since division by zero is undefined. That means 9 is excluded from g(x) as well.
Thus I would expect the domain of f(g(x)) to read [0,9)U(9,infinity).
My book/video says the domain is (9,infinity). I don't understand why values from 0 to 9 cannot be part of the domain. I see nothing stopping me from including them. Can't I plug in 4 for instance into g(x), resulting in "(2)-3" as the denominator of f(g(x))? Wouldn't that produce a negative one for the denominator which would just make the solution "-3." I don't see any way in which having 4 in the domain violates what I know is excluded.

Thank you guys for the help in advance. I really apreciate everything you guys do for me

 

[Dr.Peterson]

They only gave you those two choices?

And they said explicitly that (b) is the correct answer?

Then obviously they are wrong. Your domain [0,9)U(9,infinity) is correct.

Don't let them take away your self-confidence.

 

[ksdhart2]

I'm with Dr. Peterson on this one. I certainly hope there was additional answers that aren't shown in the image, as neither (a) nor (b) is the correct answer. What you posted: \([0, 9) \cup (9, \infty)\) is the right answer.

 

[Ebba Sen Pai]

They only gave you those two choices?

And they said explicitly that (b) is the correct answer?

Then obviously they are wrong. Your domain [0,9)U(9,infinity) is correct.

Don't let them take away your self-confidence.

Thank you both so much! They provided a total of 3 choices, but my solution was not one of them (the last was [9,infinity] ). I chopped off the final solution's answer because it was bleeding into the timestamp of the video (from my MyMathLab Ebook) and I wanted to post a relatively clear visual here so as to avoid confusion. I was tearing my hair our thinking I had missed some basic yet highly essential concept. It's great to hear that I was mislead in self doubt. MYMathLab has been incredible in previous classes, and while I would still recommend it to others, I notice that the Precalc section is making mistakes, and this confirms it in my mind. The previous mistakes weren't large, but this one revolving around them providing the wrong solution is a bit more concerning.
As always, you guys are the best!

 

[pka]

Thank you both so much! They provided a total of 3 choices, but my solution was not one of them (the last was [9,infinity] ). I chopped off the final solution's answer because it was bleeding into the timestamp of the video (from my MyMathLab Ebook) and I wanted to post a relatively clear visual here so as to avoid confusion. I was tearing my hair our thinking I had missed some basic yet highly essential concept. It's great to hear that I was mislead in self doubt. MYMathLab has been incredible in previous classes, and while I would still recommend it to others, I notice that the Precalc section is making mistakes, and this confirms it in my mind. The previous mistakes weren't large, but this one revolving around them providing the wrong solution is a bit more concerning.

I am not at all sure the meaning of the above. That said, I hope for your sake you will get yourself a better quality set of study notes. The kinds of mistakes seem above can do real harm to someone already unsure of him/herself. Please find better study-notes.

 

[ksdhart2]

As far as MyMathLab is concerned, I have no direct experience but from what I've heard it appears to be fairly reliable as far as errors in the given answers are concerned. Every now and again there will be an error, but nobody's perfect, after all. However, MyMathLab is also known for being particularly stubborn and rigid in regards to "freeform" or "fill-in-the-blank" style answers. It expects the answers to be written/formatted in exactly one way, leading many students to believe their answers to be incorrect when really they were just written "wrong."

 

[Dr.Peterson]

I've used MyMathLab with students, and agree with ksdhart2. This appears to be a different particular product (Ebook, video), which may be newer, and may be more closely tied to the particular author, both of which may be reasons for having more errors. (It's also possible for a teacher to create a special exercise, which may be more likely to have errors.)

When I have assigned the original MyMathLab (now MyLab Math), I've made it optional, and emphasize to students that if they ever can't figure out why their answer is rejected, they should use the "Ask My Instructor" feature to show me what they did, and I'd override the score if needed. (Usually it turns out that the student is actually wrong.) Many students benefit greatly from it, but others are put off by computer learning. If it works well for you in general, stick with it, but just be aware that it is human ...

 

[Ebba Sen Pai]

I've used MyMathLab with students, and agree with ksdhart2. This appears to be a different particular product (Ebook, video), which may be newer, and may be more closely tied to the particular author, both of which may be reasons for having more errors. (It's also possible for a teacher to create a special exercise, which may be more likely to have errors.)

When I have assigned the original MyMathLab (now MyLab Math), I've made it optional, and emphasize to students that if they ever can't figure out why their answer is rejected, they should use the "Ask My Instructor" feature to show me what they did, and I'd override the score if needed. (Usually it turns out that the student is actually wrong.) Many students benefit greatly from it, but others are put off by computer learning. If it works well for you in general, stick with it, but just be aware that it is human ...

Thank you for the explanation, and I completely agree. The Ebook I am using is "Blitzer College Agebra". It is by a different author than my arithmetic->Intermediate Algebra class Ebooks were. It will take alot to dissuade me of my love for MYMathLab. I have been able to deliberately and selectively take only courses with a mandatory MYMathLab component from my school. The fact that it will generate new problems for me in the "Study Section" is how I "grind" new concepts into my memory. I love instantly being told where I went wrong, and often provided an example of how to do a nearly identical problem correctly. I have heard of classes where students don't have answers in their books at all. I can imagine myself doing 50 problems incorrectly and patting myself on the back for "getting them correct" in that kind of circumstance. For me that would be the making of nightmares.

Again, thanks all for the amazing answers and support. Take care!

 

[Dr.Peterson]

I think you've identified all the good aspects of a system like MyMathLab, which can be extremely helpful for many students. Occasional errors don't detract (much) from that; textbooks have errors too, perhaps even more often. In both cases, the solution is to check both your answers and theirs, and to ask at sites like this if you think they're wrong. (Telling us exactly what's happening, including their answer, is important, so we don't go off in the wrong direction.)

By the way, I've taught from Blitzer books, and they're fine; errors in answers probably don't come from the author, but from someone else the publisher hires to do that (including programmers who generate answers to variable questions), whom you can't know anything about. You're really trusting the publisher's quality control.