Answer:
The domain of the given equation is [tex]D=[x|x\neq 13][/tex]
Step-by-step explanation:
Given : If [tex]f(x)=x+7[/tex] and [tex]g(x)=\frac{1}{x-13}[/tex]
To find : What is the domain of [tex](fog)(x)[/tex]?
Solution :
We can write,
[tex](fog)(x)=f(g(x))[/tex]
[tex](fog)(x)=f(\frac{1}{x-13})[/tex]
[tex](fog)(x)=\frac{1}{x-13}+7[/tex]
[tex](fog)(x)=\frac{1+7x-91}{x-13}[/tex]
[tex](fog)(x)=\frac{7x-90}{x-13}[/tex]
We have seen that [tex](fog)(x)[/tex] to be defined when denominator cannot be zero.
i.e. [tex]x-13\neq0[/tex]
[tex]x\neq13[/tex]
So, The domain of the given equation is [tex]D=[x|x\neq 13][/tex]
