We will have the following:
First, we are given:
[tex]f(x)=3\sqrt{6-5x}+4[/tex]
Now, to determine the domain we calculate for which value the root is 0, that is:
[tex]\begin{gathered} \sqrt{6-5x}=0\Rightarrow5x-6=0 \\ \Rightarrow5x=6\Rightarrow x=\frac{6}{5} \end{gathered}[/tex]
Now, any value greater then 6/5 will make the expression have imaginary solutions, so the domain of the expression will be:
[tex]Dom_f=(-\infty,6/5\rbrack[/tex]
This, can be seeing as follows:
