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Let the domain of f(x)=[-3,6] and the range of f(x)=[-7,4]. Find the domain and range for g(x)=3f(x²).

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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].

User JayGatsby
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