Question 610925: what is the domain and range of g(x)=3sin2x-1
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Since any number can be used as input to the sin function, the domain of g is all real numbers.
The range, however, is a little more difficult, partly because I am not sure if that is sin(2x) (or  ). No matter which one it is, the maximum value for it is 1. That makes 3 times that value a 3. And since g then subtracts 1, the maximum value for g is 2.
The minimum value for sin(2x) is -1. 3 times that would be -3. Subtracting 1 we get -4. So the minimum value for g, if it has sin(2x), is -4.
The minimum value for is 0. 3 times that would be 0. Subtracting 1 we get -1. So the minimum value for g, if it has , is -1.
This makes the range of g: All real numbers between (correct minimum value) through 2, inclusive (meaning the minimum and maximum values are included in the range).
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