Question

Given the functions, f(x)=x^3+2 and g(x)=x-9, perform the indicated operation. When applicable, state the domain restriction. (f/g)(x)

Answer 1

The domain of (f/g)(x) considers the domains of g(x) and f(x) and makes sure that g(x)≠0

because (f/g)(x)=f(x)/g(x)
and division by 0 is not allowed

the domains of f(x) and g(x) are all real numbers
now find what make g(x)=0
0=x-9
9=x

9 is restricted from the domain
domain is all real numbers except 9


so
$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=$
$\frac{x^3+2}{x-9}$
the domain is all real numbers except for 9