Final answer:
The statement that g is the inverse function of f if (f \cdot g)(x) = x is True, as it signifies that the function g reverses the effect of function f, and they form a compositional identity.
Step-by-step explanation:
If (f \cdot g)(x) = x, we say that g is the inverse function of f if, and only if, for every x in the domain of g, f(g(x)) equals x and, conversely, for every x in the domain of f, g(f(x)) equals x. The statement implies a composition of two functions f and g. If the composition yields the original value x for every element in their shared domain, it indicates that applying g effectively reverses the effect of applying f, and vice versa, thus making g the inverse of f. Therefore, the statement is True.
However, the discussion about product and constant has no direct bearing on the truth of this statement, since the original question deals with function composition and not multiplication. If the operations were multiplicative, resulting in a constant, different logic would be applied and would not necessarily indicate that one function is the inverse of the other.