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How to find the domain of a function?

The domain of the function g(x) = f(5 - 3x) is [-2, 3], find the domain of f(x). How to find the domain of f(x)? We are given: the function g(x) has the domain of [-2, 3], that is, the independent variable x has the range of -2 <= x <= 3. Then each side of the inequalities multiply 3, we get -6 <= 3x <= 9. Each side of the inequality multiply (-1). Note: when each side of an inequalities multiply (-1), the inequalities will change its direction. Then 6 >= - 3x >= -9. Now plus 5 in each side of the inequalities, we get 11 >= 5 - 3x >= -4. Note: (5 - 3x) is the independent variable of the function f. So the domain of f(x) is [-4, 11]. This example involved in concepts of domain and function, and the skill to solve an inequality.