Answer:
Step-by-step explanation:
m (x) = (x+ 5) / (x -1) and n(x) = x - 3.
[tex]m(x) = \dfrac{x+5}{x-1}[/tex]
Hence
[tex]m(n) = \dfrac{n+5}{n-1}[/tex]
but n is a function and n = x-3. Now, replace value of n on m (n)
[tex](m(n))= \dfrac{(x-3)+5}{(x-3)-1}[/tex]
simplify it
[tex](m\bullet n)(x) =\dfrac{x+2}{x-4}\\[/tex]
since (m . n) (x) is a fraction function, its domain will be all x such that the denominator is NOT 0. That is
[tex]x-4\ne 0\rightarrow x\ne 4[/tex]
among options, only C has the same denominator with [tex](m\bullet n)(x)[/tex]
Hence their domains are the same.