Given that

$$f(x)=x^2-4,andg(x)=x+3$$

$$f(g(x))=?$$

So,

$$f(g(x))=f(x+3)=(x+3{)}^2-4=0$$

$$(x+3{)}^2=4$$

$$x+3=\pm 2$$

$$\therefore x=-1,x=-5$$