Answer:
Domain is [tex](-\infty, 0) \cup(0,3) \cup(3, \infty,)[/tex]
Solution:
As given in the problem, the rational function is,
[tex]8 \times x \times(x-3) F(x)=2-7 x-4[/tex]
[tex]F(x)=\frac{-2-7 x}{8 x(x-3)}[/tex]
We know that the rational function is simply a fraction and in a fraction the denominator cannot be equal to zero because it would be undefined,
Hence from the equation above, we can say that
[tex]F(x)=\frac{-2-7 x}{8 x(x-3)}[/tex]
[tex]8 x \neq 0 \text { and }(x-3) \neq 0[/tex]
[tex]x \neq 0 \text { and } x \neq 3[/tex]
So, the domain is [tex](- \infty, 0) \cup(0,3) \cup(3, \infty,)[/tex]
