Final answer:
To transform f(x) = 1/x into g(x) = 3/(1 + 2x), one must vertically scale f(x) by 3 and apply a combination of horizontal shift and compression by a factor of 2.
Step-by-step explanation:
The transformation applied to f(x) = 1/x to produce g(x) = 3/(1 + 2x) involves several steps. First, the function is multiplied by 3 to scale it vertically. This changes the function to 3 * f(x). Next, the inside of the function is replaced by (1 + 2x), which is a horizontal transformation involving a shift to the left and a horizontal compression by a factor of 2. Therefore, the full transformation of f(x) to g(x) includes a vertical scaling by 3, followed by a horizontal shift and compression by a factor of 2.