Final answer:
The value of f(g(x)) is 3136x² and the value of g(f(x)) is 224x². Since neither of these simplify down to x, the functions f and g are not inverse functions of each other.
Step-by-step explanation:
To find the value of f(g(x)), we substitute g(x) into the function f(x). Since f(x) = 16x² and g(x) = 14x, we get f(14x) = 16(14x)² = 16 × 196x² = 3136x². Conversely, to find g(f(x)), we substitute f(x) into g(x), resulting in g(16x²) = 14 × 16x² = 224x².
The definitions of inverse functions suggest that if f is the inverse of g, then f(g(x)) should equal x, and g(f(x)) should also equal x. In our case, f(g(x)) = 3136x² and g(f(x)) = 224x², which do not simplify down to x, indicating that f and g are not inverse functions of each other.