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)?

Answer 1

Answer:

R-{13}

Step-by-step explanation:

We are given that

$f(x)=x+7$

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

We have to find the domain of fog(x).

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

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

$fog(x)=\frac{1}{x-13}+7=\frac{1+7x-91}{x-13}=\frac{7x-90}{x-13}$

Domain of f(x)=R

Because it is linear function.

Domain of g(x)=R-{13}

Because the g(x) is not defined at x=13

fog(x) is not defined at x=13

Therefore, domain of fog(x)=R-{13}

Answer 2

Answer:

The domain is all real values of  except x = 13.

Step-by-step explanation:

(f o g)(x) =  (1/ (x - 13))  + 7.

The domain is all real numbers except x = 13.