Final answer:
To find the functions f and g from the given function h(x), we recognize f as a constant function f(x) = c within the interval 0 ≤ x ≤ 20. Without complete information, the exact form of g cannot be determined although it appears to be related to a quadratic expression.
Step-by-step explanation:
To find the functions f and g given the function h(x) = 6x² + 6x + 2⁴, we need to understand what is being asked. For the function f, it must create a horizontal line when graphed, which means it's a constant function. Given the restrictions 0 ≤ x ≤ 20, we can write f(x) = c, where c is the constant value of the function on that interval. For the function g, we infer from the examples given that it might be related to the standard form of a quadratic equation ax² + bx + c. However, without further context or additional equations, we cannot determine the exact form of g.
To illustrate, an example of a constant function is f(x) = 20 for 0 ≤ x ≤ 20. This satisfies the condition that the graph of f(x) is a horizontal line within the given interval. As for g, if it relates to the provided example (181²) = g(t- 1)², we might deduce that g is a function whose output will be squared and equal to a constant or another function value when t is substituted for x. However, the missing context prevents us from providing an exact function for g.