Solve for: f(x)=sqrt(3x-6)

Expression: $f\left( x \right)=\sqrt{ 3x-6 }$

Separate the function into parts to determine the domain of each part

$\begin{array} { l }\sqrt{ 3x-6 },\\3x-6\end{array}$

The domain of an even root function are all values of $x$ for which the radicand is positive or $0$

$\begin{array} { l }x \geq 2,\\3x-6\end{array}$

The domain of a linear function is the set of all real numbers

$\begin{array} { l }x \geq 2,\\x \in ℝ\end{array}$

Find the intersection

\begin{align*}&x \in \left[ 2, +\infty\right\rangle \\&\begin{array} { l }x \geq 2\end{array}\end{align*}

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