Question

If f(x) = 3 – 2x and g(x)=1/x+5, what is the value of (f/g)(8)?

Answer 1

f(x) = 3 - 2x
g(x) = 1/(x + 5)

(f/g)(x) = (3 - 2x) / 1/(x + 5) = (3 - 2x)(x + 5)
(f/g)(8) = (3 - 2(8))(8 + 5) = -13 x 13 = -169

Answer 2

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
`(f)/(g)` 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.

`(f/g)(x) =`
`(f(x))/(g(x))`

Given: f(x) = 3-2x and g(x) =
`(1)/(x+5)`

Then, using arithmetic combination of function definition:

`(f/g)(8)=(f(8))/(g(8))` ......[1]

Now, first find the value of f(9) and g(8) ;

f(8) =3-2(8) = 3-16 = -13 and

`g(8) =(1)/(8+5) =(1)/(13)`

Substitute these in equation [1] ;

`(f/g)(8) =(-13)/((1)/(13)) = -13 * 13 =-169`

Therefore, the value of (f/g)(8) is; -169