Let fx 3x2 4 and gx x 3 a Find the composite function f

Let f(x) = 3x^2 - 4 and g(x) = x - 3. (a) Find the composite function (f compositefunction g) (x) and simplify. Show work. (b) Find (f compositefunction g) (-2). Show work.

Solution

f(x) = 3x^2-4 and g(x)=x-3

(fog)(x) = f(g(x))

            = f(x-3)

            = 3(x-3)^2-4

             = 3(x^2-6x+9)-4

              =3x^2-18x+27-4

              = 3x^2-18x+23

(fog)(-2) = 3(-2)^2-18(-2)+23

             =12+36+23

            =71