if f(x)=x^2-4x and g(x)=2x+3, express (fog)(x) in simpliest form?

f(x) = x^2 - 4x

g(x) =
2x+3

We need to find the equation of
fog(x).

We know that fog(x) =
f(g(x)).

We will substitute with g(x) =
2x+3

==> f(g(x)) = f(
2x+3)

Now we will substitute with x= 2x+3 into
f(x).

==> f(g(x)) = g(x)^2 -
4g(x)

                   = (2x+3)^2 -
4(2x+3)

                    = 4x^2 + 12x + 9 - 8x -
12

Now we will combine like
terms.

==> f(g(x)) = 4x^2 +4x -
3

Then fog(x) = 4x^2 + 4x -3
.