Solution:
The function is given below as
[tex]\begin{gathered} g(x)=\frac{x+4}{x-1} \\ h(x)=2x-1 \end{gathered}[/tex]
To figure out
[tex](goh)(x)[/tex]
To do this , we will substitute x= 2x-1 in g(x)
[tex]\begin{gathered} g(x)=\frac{x+4}{x-1} \\ g(h)(x)=\frac{2x-1+4}{2x-1-1} \\ g(h)(x)=\frac{2x+3}{2x-2} \end{gathered}[/tex]
Hence,
The composte function will be
[tex](goh)(x)=\frac{2x+3}{2x-2}[/tex]
Step 2:
To figure out the domain,
In mathematics, the domain of a function is the set of inputs accepted by the function.
Hence,
The domain of the function is
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x<1\quad \mathrm{or}\quad \:x>1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:1\right)\cup \left(1,\:\infty \:\right)\end{bmatrix}[/tex]
