Let fx 9x2 4 and gx x 2 a Find the composite functionf g

Let f(x) = 9x^2 - 4 and g(x) = x - 2. (a) Find the composite function(f g)(x) and simplify. Show work. (b) Find (f g)(-1). Show work.

Solution

f(x) = 9x² - 4

g(x) = x - 2

a) (f o g) (x) = f(g(x))

                    = 9 * (g(x))² - 4

                    = 9 * (x - 2)² - 4

                   = 9 (x² + 4 - 4x) - 4

                   = 9x² -36x + 36 - 4

                  = 9x² -36x + 32 (ans)

b) (f o g) (-1) = 9 * (-1)² - 36 * (-1) + 32

                     = 77 (ans)