[tex]log(x - 1) + 2[/tex]
Domain:
The condition of log functions, is to set what's in between the brackets as being strictly greater than 0.
[tex]x - 1 > 0[/tex]
[tex]x > 1[/tex]
Domain:
[tex]1 < x < \infty [/tex]
Range:
The range of log functions is all real numbers:
[tex] - \infty < f(x) < \infty [/tex]