Find the domain of the coposite function f∘g f(x)=5x+9 g(x)=x+6

The value of ${\displaystyle f\circ g}$ is:
${\displaystyle f\left(g\left(x\right)\right)=f(x+6)}$
${\displaystyle =\frac{5}{(x+6)+9}}$
${\displaystyle =\frac{5}{x+15}}$
therefore the composite function fog is:${\displaystyle f\left(g\left(x\right)\right)=\frac{5}{x+15}}$
as we know that the domain of the function is the set of values of the independent variable for which the function is defined.
so we can notice that the composite function ${\displaystyle f\circ g}$ is defined when the denominator of ${\displaystyle f\circ g}$ is not equal to zero.
that implies
${\displaystyle x+15\ne 0}$
${\displaystyle x\ne -15}$
therefore the composite function ${\displaystyle f\circ g}$ is defined for all values of x except x=-15.
therefore the domain of the composite function ${\displaystyle f\circ g}$ is ${\displaystyle :\{x\mid x\ne -15\}}$
therefore the second option is correct.