Let f (x) = 9x^2 + 7 and g(x) = x + 2.

Question

(a) Find the composite function(f of g)(x) and simplify. Show work.
(b) Find (f of g)(-3). Show work.

Answer 1

a)

 

f(g(x)) =

 

f(x + 2)

 

 

Plug in x + 2 into x in function f.

 

f(x + 2) = 9(x + 2)² + 7

            = 9(x² + 4x + 4) + 7

            = 9x² + 4x + 43

           

 

b)

 

 

f(g(-3)) = f(-3 + 2)

             = f(-1)

             = 9(-1)² + 7

             = 9 + 7

             = 16