Here we have function
[tex]g(x)=3log_{2}(x-1)+2[/tex]
Domain is the set of values for which the function is defined ( should have finite value)
Let us find the value of x for which g(x) is not defined
g(x) is logarithmic function and log of 0 and negative numbers are not defined,
so we have
[tex]x-1> 0[/tex]
[tex]x>1[/tex]
hence the domain is all real number greater than 1
