Final answer:
The domain of g(x) is [-3^2, 6^2] = [0, 36], and the range of g(x) is [63, 48].
Step-by-step explanation:
The domain of a function represents the possible input values, while the range represents the possible output values. To find the domain and range for g(x) = 3f(x^2), we need to consider the domain and range of f(x) and apply the given transformation.
Since the domain of f(x) is [-3, 6], the domain of g(x) = 3f(x^2) is the set of all numbers that can be obtained by squaring numbers in the domain of f(x) and then multiplying them by 3. Therefore, the domain of g(x) is [-3^2, 6^2] = [0, 36].
Next, to determine the range of g(x), we need to consider the range of f(x) and apply the transformation. Since the range of f(x) is [-7, 4], when we square the values in the range of f(x) and then multiply them by 3, we get the range of g(x) as [3*(-7)^2, 3*4^2] = [63, 48].