Expert: Paul Klarreich - 11/12/2008

Question
Kindly help with the following:

1. Let f(b)= a^2b^3 + a^3b^2 what is f(a)? and what is f(ab)?
2. TR = f(q)=1760q-12q^2 what is f(q+h) -f(q) ..h is just a small unknown numner

Answer
Questioner:   Tunde
Category:  Advanced Math

Subject:  Algebra
Question:  Kindly help with the following:
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Hi, Tunde,

1. Let f(b)= a^2b^3 + a^3b^2 what is f(a)? and what is f(ab)?

When you use function notation, ALWAYS ALWAYS ALWAYS ALWAYS ALWAYS ALWAYS ALWAYS follow this procedure:

A. Write the function definittion with empty parentheses in place of the argument, everywhere you see it.  

In f(b)= a^2b^3 + a^3b^2, the argument is what you see after the function name [here it is f] and inside the parentheses.  In this case the argument is b.  The argument is nothing but a placeholder -- it has no meaning of its own.

Write:  f( ) = a^2( )^3 + a^3( )^2

No exceptions! Write it EXACTLY LIKE THAT, every time.

Now insert the substitution.  

If you want f(a), the substitution is a.
f( ) = a^2( )^3 + a^3( )^2
f(a) = a^2(a)^3 + a^3(a)^2

Simplify.  I leave that to you.  Do whatever algebra is indicated.

If you want f(ab), the substitution is ab.
f( ) = a^2( )^3 + a^3( )^2
f(ab) = a^2(ab)^3 + a^3(ab)^2

Likewise.
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2. TR = f(q)=1760q-12q^2 what is f(q+h) -f(q) ..h is just a small unknown number
 
What is that TR?  

Anyway, if you follow the steps in part 1, you should have no trouble with this.  If you do, send along what you tried.
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P.S. Don't mark private on your questions.  I change it anyway, and if you really want it to be invisible, send it somewhere else.