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Answer:
{f(x), g(x)} = {x^4, x(x+4)}
Step-by-step explanation:
If we look at the composite function from the point of view of the Order of Operations, we see the operations performed on x are ...
- x is squared
- x is multiplied by 4
- these products are added
- the sum is raised to the fourth power
From the point of view of decomposition, we want the outer function (f(x)) to be one that can be applied to the expression produced by the inner function (g(x)). Looking at our list, we find that raising an expression to the 4th power could qualify as the outer function we want. (We could also use raising to some other power, if we wanted.)
So, f(x) = x^4.
This leaves ...
f(g(x)) = f(4x +x^2)
so, g(x) = 4x +x^2.
One possible set of functions is ...
{f(x), g(x)} = {x^4, x(x+4)}
