Final answer:
To find f(x) and g(x) such that h(x) = (f o g)(x) = 2/(x-3)⁶, one possible solution is g(x) = x - 3, and f(x) = 2/x⁶. Composing these gives the desired h(x) function.
Step-by-step explanation:
To find functions f(x) and g(x) such that h(x) = (f o g)(x), we need to find two functions that when composed give h(x) = 2/(x-3)⁶. A reasonable choice would be to let g(x) be a function that transforms x into the form present in the denominator of h(x), and let f(x) be a function that formats the output into the desired form of h(x).
One possible pair of functions could be:
g(x) = x - 3: This function shifts the input x by 3 units.
f(x) = 2/x⁶: This function takes the input (assumed to be g(x)) and raises it to the power of -6 before multiplying by 2.
Thus, (f o g)(x) = f(g(x)) = f(x - 3) = 2/(x - 3)⁶, which is equal to the given h(x).