For this case we have the following functions:
[tex]f (x) = x + 7\\g (x) = \frac {1} {x} -13[/tex]
We must find [tex](f_ {0} g) (x).[/tex] By definition we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {0} g) (x) = \frac {1} {x} -13 + 7 = \frac {1} {x} -6[/tex]
By definition, the domain of a function is given by all the values for which the function is defined.
The function [tex](f_ {0} g) (x) = \frac {1} {x} -6[/tex] is no longer defined when x = 0.
Thus, the domain is given by all real numbers except zero.
Answer:
x nonzero
