Final answer:
To find two nontrivial functions f(x) and g(x) such that f(g(x)) = -(x - 10)^2, we can let g(x) = x - 10 and f(x) = -x^2.
Step-by-step explanation:
In order to find two nontrivial functions f(x) and g(x) such that f(g(x)) = -(x - 10)2, we can start by considering what the equation represents. It is a composition of functions, where g(x) is being plugged into f(x). This means that the output of g(x) is the input for f(x).
We can let g(x) = x - 10 and f(x) = -x2. By plugging g(x) into f(x), we get f(g(x)) = -((x - 10)2) = -(x - 10)2 as desired. Therefore, g(x) = x - 10 and f(x) = -x2 represent two nontrivial functions that satisfy the given equation.