What are the domain and range of f of x is equal to the log of open paren x minus 1 close paren plus 2 ?

For f(x) = log(x − 1) + 2, the expression inside the logarithm must be positive: x − 1 > 0, so the domain is x > 1. A logarithm can produce any real number, and adding 2 shifts its outputs without restricting them, so the range is all real numbers. Thus, the correct choice is “domain: x is greater than 1; range: all real numbers.”

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