Answer:
Domain = R- {0,4}
Step-by-step explanation:
[tex]f(x) =\frac{3x-1}{x-4}[/tex]
[tex]g(x) =\frac{x+1}{x}[/tex]
[tex](f*g)(x)=\frac{3x-1}{x-4} \times \frac{x+1}{x}[/tex]
[tex](f*g)(x)=\frac{(3x-1)(x+1)}{(x-4)(x)}[/tex]
In order to function (f*g)x to be defined , the Denominator must not be equal to zero.
Hence
x ≠ 0
(x-4) ≠ 0 ⇒ x≠4
Hence (f*g)x is defined for all values of x except 0 and 4
Hence Domain = R- {0,4}
