Question

If f (x) = x + 7 and g (x) = StartFraction 1 Over x minus 13 EndFraction, what is the domain of (f circle g) (x)? StartSet x vertical line x not-equals 6 EndSet StartSet x vertical line x not-equals negative 6 EndSet StartSet x vertical line x not-equals negative 13 EndSet StartSet x vertical line x not-equals 13 EndSet

Answer 1

Answer:

The domain of the function will be {x I x ≠ 13}.

Step-by-step explanation:

The two functions f(x) and g(x) are given to be

f(x) = x + 7 and

$g(x) = \frac{1}{x - 13}$

Now, we have to find the composite function (fog)(x).

Here, (fog)(x) = f{g(x)}

⇒ $(fog)(x) = f(\frac{1}{x - 13}) = \frac{1}{x - 13} + 7 = \frac{7x - 90}{x - 13}$

Therefore, the denominator of the function can not be zero and the domain of the function will be {x I x ≠ 13}. (Answer)

Answer 2

The domain of the function (fog)(x) will be {x$\epsilon$R | x  $\neq$ 13} and this can be determined by evaluating the function (fog)(x).

Given :

• $\rm f(x) = x+7$

• $\rm g(x) = \dfrac{1}{x-13}$  

To determine the domain of function (fog)(x), first, evaluate the function (fog)(x).

(fog)(x) = f(g(x))

           $\rm =f(\dfrac{1}{x-13})$

           $=\dfrac{1}{x-13}+7$

           $=\dfrac{1+7x-91}{x-13}$

            $=\dfrac{7x-90}{x-13}$

$(fog)(x)=\dfrac{7x-90}{x-13}$

Therefore, the domain of the function (fog)(x) will be {x$\epsilon$R | x  $\neq$ 13} and this can be determined by evaluating the function (fog)(x).

For more information, refer to the link given below:

https://brainly.com/question/2263981