we have the function
[tex]y=\sqrt[\square]{x-1}-4[/tex]Remember that the radicand must be positive
so
[tex]\begin{gathered} x-1\ge0 \\ x\ge1 \end{gathered}[/tex]therefore
the domain is the interval [1, infinite)
Find out the range
For x=1
y=-4
so
the range is
[tex]y\ge-4[/tex]