Answer:
Option 2 is correct.
Step-by-step explanation:
We are given the functions,
[tex]f(x)=x^3+2[/tex]
[tex]g(x)=x-9[/tex]
Then, we get that,
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
i.e. [tex](\frac{f}{g})(x)=\frac{x^3+2}{x-9}[/tex]
Thus, the quotient function is [tex]\frac{x^3+2}{x-9}[/tex].
Since, the functions in the numerator and denominator are polynomial.
So, they both are defined for all real numbers.
But, as the quotient function is not defined for x= 9.
Thus, the domain for the quotient function is 'Set of real numbers excluding 9'.
Hence, option 2 is correct.
