ANSWER
[tex][6,\infty)[/tex]EXPLANATION
We want to identify the domain of the function:
[tex]f(x)=(6x-36)^{\frac{1}{2}}[/tex]Let us write the function:
[tex]f(x)=\sqrt{6x-36}[/tex]The domain of a function is the set of all x values for which the function is valid.
The given function contains a radical (square root). A radical is invalid if the radicand (the expression inside the radical) is less than 0.
This implies that the radicand must be greater than or equal to 0:
[tex]6x-36\ge0[/tex]Now, solve for x:
[tex]\begin{gathered} 6x\ge36 \\ \\ x\ge\frac{36}{6} \\ \\ x\ge6 \end{gathered}[/tex]Hence, the domain of the function is:
[tex]x\ge6[/tex]In interval notation, the domain is:
[tex][6,\infty)[/tex]