Final answer:
The correct form of the equation is option (a), 6x h(h(g(x))) = 468x - 72, as given in the question itself. Additional context or functions for 'h' and 'g' are needed for further simplification or transformation.
Step-by-step explanation:
The correct form of the equation 6x h(h(g(x))) = 468x - 72 is actually the one presented in the question itself, which is option (a). However, the question also seems to introduce concepts that are not directly related, such as working with exponents, quadratic equations, and manipulating equations with parentheses, which can be used to solve various types of algebraic expressions. We're given the original equation and asked to determine the correct form by potentially isolating terms; however, without additional context or functions for 'h' and 'g', we cannot simplify or transform the equation further. It's also important to note that dividing by 'h' as seen in some of the other options would only be valid if 'h' were a constant, but we do not have enough information to make that determination.The correct form of the equation is 6x h(h(g(x))) = 468x - 72 (option a).
To reach this conclusion, we need to solve the equation step by step. First, we expand the equation by applying the operations:
6x h( (h(g(x))) ) = 468x - 72
6x ( g(x) ) = 468x - 72
6xg(x) = 468x - 72
6xg(x) - 468x = -72
-396xg(x) = -72
g(x) = -72 / -396x
g(x) = 1/11x
Therefore, the correct form of the equation is 6x h(h(g(x))) = 468x - 72 (option a)