Answer: OPTION D
Step-by-step explanation:
We know that the function [tex]y=log(x)[/tex] is not defined for values of x less or equal than zero, therefore its domain is [tex](x|x>0)[/tex] and the range is all real numbers.
In this case we have the function [tex]y=log(x-2)+1[/tex], then [tex]x-2[/tex] must be greater than zero.
Then:
[tex]x-2>0\\\\x>2[/tex]
Therefore, the domain of the function is:
[tex]x>2[/tex] or [tex](2, \infty)[/tex]
And the range is:
All real numbers.
