Final answer:
The domain and range of the function f(x) = logg(x - 1) 3 are (1, infinity) and (-infinity, infinity) respectively. The domain is determined by all possible x-values, and the range is determined by all potential results of the logarithmic function
Step-by-step explanation:
The function given is f(x) = logg(x - 1) 3. The domain of this function refers to all possible values of x, while the range refers to all possible outputs of the function.
Because this is a logarithmic function, the domain is restricted to where the input x is greater than 1, because you cannot take the log of a negative number or zero. So the domain of this function is (1, infinity).
The range of a logarithmic function, however, is any real number, because log(x - 1) can return any real number as a result. So, the range of this function is (-infinity, infinity).
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