ANSWER
domain: x > 1; range: all real numbers
EXPLANATION
The given logarithmic function is
![f(x) = log(x - 1) + 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/s029q1qyhpzt8j8yco4fs894y2ndjk4ehu.png)
The domain of this function refers to all values of y for which x is defined.
This function is defined argument is greater than 1.
![x - 1 \: > \: 0](https://img.qammunity.org/2020/formulas/mathematics/middle-school/aynwzd2nwizz62xg72qcdo8gsu3f5qxlzp.png)
![x \: > \: 1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yoa8w3w0x9fw4c9uwmirfhp986jkelxeh6.png)
The range refers to all values of y for which x is defined.
x is defined for all values of y.
The range is all real numbers.