Question

Suppose that the functions f and g are defined as follows. f(x)= x-6/x+5 g(x)= x/x+5. find f/g. Then, give its domain using an interval or union of intervals. simplify your answers.

Answer 1

STEP 1:

To find f/g we divide f(x) by g(x)

`(f)/(g)=((x-6)/(x+5))/((x)/(x+5))\text{ = }(x-6)/(x+5)\text{ }*\text{ }(x+5)/(x)\text{ =}(x-6)/(x)`

Therefore the value of f/g is

`(f)/(g)=(x-6)/(x)`

STEP 2:

Also, the domain is the set of all possible x-values which will make the function "work", and will output real values.

The domain of this function is

`-\infty<strong>This implies that the function would exist for all values of x except when x=0</strong><p>The above domain can also be represented as :</p>[tex](-\infty,0)\text{ and (0,}\infty)`