Question

The domain of g(f(x)) is:

Answer 1

$\begin{gathered} f(x)=3x-1 \\ g(x)=\sqrt[]{x} \\ so\colon \\ g(f(x))=\sqrt[]{3x-1} \end{gathered}$

the square root must be positive, so:

$\begin{gathered} 3x-1\ge0 \\ 3x\ge1 \\ x\ge\frac{1}{3} \end{gathered}$

the domain of g(f(x)) is:

$D\colon x\ge\frac{1}{3}$