Try expressing in terms of .
or
or
or
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?
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 one-to-many relation and therefore not a function.)