Answer:
[tex]x\geq 5[/tex]
Step-by-step explanation:
The function that we have to study in this problem is
[tex]y=\sqrt{x-5}-1[/tex]
The domain of a function is defined as the set of all the possible values of x that the function can take.
For a square-root function, there are some limitations to the possible value of the argument in the root.
In particular, the argument of a square root must be equal or greater than zero, because the square root of a negative number is not defined.
Therefore, in this case, we have to set the following condition for the domain:
[tex]x-5\geq 0[/tex]
And by solving, we get
[tex]x\geq 5[/tex]
which means that the domain of this function is all real numbers equal or greater than 5.
