Final answer:
g(f(x)) = 3 / (6x) To find g(f(x)), replace x in g(x) with the expression for f(x), which yields g(6x) = 3 / (6x).
Explanation:
When evaluating g(f(x)), it means plugging the function f(x) into g(x). In this case, f(x) = 6x and g(x) = 3/x. So, substituting f(x) into g(x) results in g(f(x)) = g(6x). To find g(f(x)), replace x in g(x) with the expression for f(x), which yields g(6x) = 3 / (6x).
By substituting f(x) = 6x into g(x) = 3/x, we obtain the composite function g(f(x)) = 3 / (6x), showcasing the result of applying g to the function f(x).
This process involves replacing the variable in the inner function (f(x)) with the expression given for f(x) in the outer function (g(x)). Consequently, g(f(x)) simplifies to 3 divided by the product of 6 and x.
The composition of functions involves substituting one function into another and operating them accordingly. Here, f(x) = 6x is put into g(x) = 3/x, resulting in g(f(x)) = 3 / (6x), representing the final expression after evaluating the composite function.
This approach demonstrates how to compute the composition of functions by integrating the given expressions systematically and deriving the resultant function step by step.