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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.

Suppose that the functions f and g are defined as follows fx x6x5 gx xx5 find fg Then give its domain using an interval or union of intervals simplify your answ class=

Respuesta :

STEP 1:

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

[tex]\frac{f}{g}=\frac{\frac{x-6}{x+5}}{\frac{x}{x+5}}\text{ = }\frac{x-6}{x+5}\text{ }\times\text{ }\frac{x+5}{x}\text{ =}\frac{x-6}{x}[/tex]

Therefore the value of f/g is

[tex]\frac{f}{g}=\frac{x-6}{x}[/tex]

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

[tex]-\inftyThis implies that the function would exist for all values of x except when x=0

The above domain can also be represented as :

[tex](-\infty,0)\text{ and (0,}\infty)[/tex]

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