Final answer:
To assess whether h(x) is equivalent to (f·g)(x), we need to know how functions f and g interact to produce h(x) and if h(x) denotes their product specifically. Without explicit forms of the functions or clear definitions, we cannot determine equivalence conclusively.
Step-by-step explanation:
To determine whether h(x) is equivalent to the product function (f·g)(x), one needs to understand the nature of the expressions. The product of two functions, denoted as (f·g)(x) = f(x)·g(x), means that you multiply the outputs of f and g at a particular value of x.
Therefore, if h(x) represents the product of f(x) and g(x), it must perform that exact operation. However, if the product of f and g always equals a constant, f and g are inversely related such that when one function's output is smaller, the other's is larger to maintain a constant product. This suggests a specific type of relationship between f and g.
Turning to algebra, let's consider the implications of the equation A × F = B × F. If we divide both sides by F and F is not equal to 0, we can conclude that A = B. So, if the product of f(x) and g(x) equals h(x) for all x, and f(x) is not zero, then g(x) would be the function such that h(x) = f(x)·g(x).
Therefore, without additional information about the functions f, g, and h, we cannot conclusively say whether h(x) is equivalent to (f·g)(x). It's essential to analyze the definitions of these functions or have their explicit forms to make a conclusive statement.
If h(x) simply denotes the product of f and g, yes, it is equivalent; but if h(x) is defined differently, then it might not be.