The difference between the product of two function and composition of them is fairly big. When one multiplies two functions, that is just that, multiplication. However a composition requires that the inner function be substituted for “x” in the outer function. In such a case of f(g(x)), then g(x) must be plugged into every “x” in the function f(x). Such a composition yields a very different result than does the product of these two functions. With the product, one has to perform multiplication and is quite simply done. With the composition one must substitute the inner function for all the outer function’s “x” so that g(x) is f(x)’s new “x”; and more often than not, one is left with a function that is quite different from the product. The difference between the two is great and each is completed differently.
Question: How did Logarithms initially become implemented into Math?
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