Solving for Unknown Variables (r0q)(1) and (q0r)(1) in a Complex Equation

[nate1936]

Homework Statement

This problem is giving me issues, mainly because of how it is set up.

Homework Equations

Here is a picture of what my problem is,
http://img23.imageshack.us/img23/1723/heko.png

The Attempt at a Solution

I am attempting to solve this problem, and I haven't encountered anything like it in the book so far, I'm assuming I take the variables "q of x" and "r of x", but when solving, why are they swapped around? Is the (r0q)(1)= and (q0r)(1)= representing multiplication? I haven't seen that raised circle in the middle before. I'm assuming it has something to do with logarithms? I don't need anyone to show me how this particular problem is solved, [that would be cheating though it doesn't really matter to much in this class, 90% of the grade is based on the test]

If someone could change the variables and numbers, and/or just go through the steps on how I should go about solving this type of problem, I would really appreciate it.

 

[ArcanaNoir]

Well this is the composition of functions, which is not commutative. That mean qor (using o as the symbol of composition for lack of a better button) does not necessarily equal roq.

Do you know how to find q of r, ignoring the 1 for now?

 

[HallsofIvy]

The crucial point is, do you know the definition of "$f\circ g(x)$"? This is known as the "composition of functions". If this is the first course in which you have seen it, I'll bet there's a definition in the same section of the book in which the problem occurs!

 

[nate1936]

Thank you for your help so far, because I now know it is a "Composition of functions" problem I was able to find out how to get started with this I think.
r o q (1) can be re-written as (r(q(1)) from here, can I have a hint as to what the next step is?
If the (1) were an x I would substitute in the variables and solve for x, however I'm not sure what to do with the (1)

 

[ArcanaNoir]

You can find q(1) first and then use that in r(x), or you can first find q of r as if you only had an x, and then substitute the 1 in the final step. Try both, you should get the same answer both times.

 

[nate1936]

Is there a special function you are talking about when you say find q(1) [in the first way to solve it you have posted] or are you just multiplying the q (x) variable times one?

Sorry for my stupid questions, I have to figure this out somehow though!

 

[SammyS]

Is there a special function you are talking about when you say find q(1) [in the first way to solve it you have posted] or are you just multiplying the q (x) variable times one?

Sorry for my stupid questions, I have to figure this out somehow though!

To find q(1), substitute 1 in for the x that is given in the definition of q(x).

$q(x)=x^2+3$

 

[nate1936]

edit: nevermind I found a forum with much more straightforward answers. Thanks anyway

 

[HallsofIvy]

Did you find a forum that will take your tests for you? Getting the answer to homework problems from others, rather than working them out for yourself is a sure way to fail a course.

 

[nate1936]

Actually I found a forum that instead of side tracking and telling me what I already know, actually showed me an example problem, and showed me the steps required to solve this type of problem. I learn in a different way than the community involved on this board apparently. Sorry if that offends you.