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The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair.

Function 1

Function 2

f(x) = −x2 + 4x + 1

Function 1 has the larger maximum at (4, 1).
Function 1 has the larger maximum at (1, 4).
Function 2 has the larger maximum at (2, 5).
Function 2 has the larger maximum at (3, 2).

Function 2

Step-by-step explanation:

9514 1404 393

  {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 ...

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)}