[tex]\hbox{ range of } \sqrt {x-1} \hbox{ is } \langle0,\infty)\\
\hbox{ range of } -\frac{3}{4}\sqrt {x-1} \hbox{ is } \langle-\frac{3}{4}\cdot0,-\frac{3}{4}\cdot\infty)=(-\infty,0\rangle\\
\hbox{ range of } -\frac{3}{4}\sqrt {x-1}+4 \hbox{ is } (-\infty+4,0+4\rangle=(-\infty,4\rangle\\
[/tex]
