Solve for x. f(g(x))=0 f(x)=x^2-4 and g(x)=(x+3)

We'll substitute g(x) by it's
expression:

f(g(x)) =
f((x+3))

 f((x+3)) = (x+3)^2 -
4

We'll expand the square and we'll
get:

 f((x+3)) = x^2 + 6x + 9 -
4

 f((x+3)) = x^2 + 6x +
5

We'll solve the
equation:

 f((x+3)) = 0 <=> x^2 + 6x + 5 =
0

We'll apply the quadratic
formula:

x1 = [-6+sqrt(36 -
20)]/2

x1 = (-6 + 4)/2

x1 =
-1

x2 = -5

The
solutions of the equation f(g(x))=0 are: {-1 ;
-5}.