Final Answer:
If ( F(x) ) and ( G(x) ) are associated with each other, then ( F(x) ) is dependent on ( G(x) ).
Step-by-step explanation:
When we say that ( F(x) ) and ( G(x) ) are associated or related, it implies a certain level of dependence between the two functions. In mathematical terms, if the value of ( G(x) ) influences or affects the value of ( F(x) ), we can express this relationship as ( F(x) = f(G(x)) ), where ( f ) is some function that depends on ( G(x) ). This indicates that the function ( F(x) ) is explicitly dependent on the values of ( G(x) ).
To illustrate this point, consider an example where ( F(x) ) represents the total cost of a product and ( G(x) ) represents the quantity of that product. In this case, ( F(x) ) would be a function of ( G(x) ), as the total cost is directly influenced by the quantity purchased. Mathematically, we could write
, where ( C ) is the cost per unit. This dependency highlights the connection between the two functions.
In summary, when ( F(x) ) and ( G(x) ) are associated, it implies a dependence of ( F(x) ) on ( G(x) ), meaning changes in the values of ( G(x) ) directly affect the values of ( F(x) ). This relationship is fundamental in understanding the interplay between different mathematical functions.