Final answer:
The rule for the composition g o f (g of f) can be found by substituting f(x) into g(x) and simplifying the expression.
Step-by-step explanation:
The rule for the composition g o f (g of f) can be found by substituting f(x) into g(x). Since f(x) = -9, we substitute -9 into g(x) to get g(-9).
g(x) = 4x2/3
g(-9) = 4(-9)2/3
To simplify the expression, we first evaluate (-9)2/3. This can be written as (-1 * 9)2/3. Using the property that (a * b)c = ac * bc, we get (-1)2/3 * 92/3.
Since (-1)2/3 is equal to 1 and 92/3 is equal to 3, the expression simplifies to 1 * 3 = 3. So, g(-9) = 4(3) = 12.