Answer:
An Arithmetic Combination states that two functions f and g at any x i.e in the domain of both f and g, with one exception.
The quotient [tex]\frac{f}{g}[/tex] is not defined at values of x, where g is equal to 0 or we can say that both the functions must be defined at a point for the combination to be defined.
[tex](f/g)(x) =[/tex] [tex]\frac{f(x)}{g(x)}[/tex]
Given: f(x) = 3-2x and g(x) = [tex]\frac{1}{x+5}[/tex]
Then, using arithmetic combination of function definition:
[tex](f/g)(8)=\frac{f(8)}{g(8)}[/tex] ......[1]
Now, first find the value of f(9) and g(8) ;
f(8) =3-2(8) = 3-16 = -13 and
[tex]g(8) =\frac{1}{8+5} =\frac{1}{13}[/tex]
Substitute these in equation [1] ;
[tex](f/g)(8) =\frac{-13}{\frac{1}{13}} = -13 \times 13 =-169[/tex]
Therefore, the value of (f/g)(8) is; -169
