This has nothing to do with trigonometry.
[tex]\left(\frac fg\right)(x)[/tex] is notation for the quotient of the two functions [tex]f,g[/tex]. In other words,
[tex]\left(\dfrac fg\right)(x)=\dfrac{f(x)}{g(x)}[/tex]
The domain is the set of values of [tex]x[/tex] such that this quotient is defined. In particular, the function is defined as long as the denominator is not 0. This happens for
[tex]g(x)=x^2+4x-5=(x+5)(x-1)=0\implies x=-5,x=1[/tex]
so [tex]x[/tex] can be any value except these two. In interval notation, the domain would be
[tex](-\infty,-5)\cup(-5,1)\cup(1,\infty)[/tex]
so the answer is B (the second option).
