When there is a problem that states: Express the function in the form f(g(x)) and for example we take this function F(x) = (2x + x^2)^4
Wouldn't it be technically correct to put it as
f(x) = x and g(x) = (2x + x^2)^4

Question

When there is a problem that states: Express the function in the form f(g(x)) and for example we take this function F(x) = (2x + x^2)^4 
Wouldn't it be technically correct to put it as
f(x) = x and g(x) = (2x + x^2)^4

steve816 · Answer

Also, I'm having trouble solving these types of problems, as they are very intuitive and kind of like a puzzle. Any help?

will.h · Answer

They are pretty easy See the example below and if you still have trouble inform me 

Suppose we have the following example f(x) = 10x + 2
g(x) = 2x +3

We want to derive the following equation f((gx))

What you need to do is simplify bring the required function in parentheses 
so (2x + 3) and now see that f(x) has a constant of + 2 so you need to add that and a leading coefficient of 10 so you need to distribute that so we have now 

10(2x + 3) +2 = f((gx)) Simplify and that's what we get

20x + 32 = f((gx)) 

Hope that helps.

holsteremission · Answer

Setting $f(x)=x$ and $g(x)=(2x+x^2)^4$ would be the easiest approach. It's certainly correct that $F(x)=f(g(x))$ but it's probably not the solution the author had in mind.

The next obvious choice would probably be to decompose the composition into its "outer-" and "innermost" components. In this case, you could use $f(x)=x^4$ and $g(x)=2x+x^2$.