
Functions of functions
its easy to plug a function into a function, we did that in algebra.
f(x)=x^2 g(x) = (x+2) fog(x)= x^2+4x+4
but how about going the other way
if fog(x)= 3x^2+2x+8 and g(x) = (x^2+4x), what is f(x)?
I never learned this in precalc or algebra, which branch or course deals with this topic? What is the process for solving these kind of problems?

Try expressing in terms of .
or
or
or

Be careful here! You get two different functions depending on what domain you choose for .
If you choose as your domain for , then and so .
If you choose as your domain for , then .
(In both cases, the domain of is .)
However, if you choose as your domain for , then, unfortunately, it will be impossible to determine as a function. ( would be a onetomany relation and therefore not a function.)