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.