1. Composition of Functions

2. Definition of Composition of Functions The composition of the functions f and g are given by (f o g)(x) = f(g(x))

3. (f o g)(x) is read as f composed of g

4. Steps in computing (f o g)(x) 1. Begin with the f function. 2. Plug the g formula in for x. 3. Complete the f formula. 4. Reduce the equation.

5. Suppose f (x) = x 2 + 3 g(x) = 4x

6. (f o g) (x) = f(g(x)) Plug the g formula in for x in the f formula f(4x) = (4x) 2 + 3 = 16x 2 + 3

7. (g o f) (x) = g(f(x)) Plug the f formula in for x in the g formula g(x 2 +3) = 4(x 2 + 3) = 4x 2 + 12

8. Recall f(x) = x 2 + 3 and g(x) = 4x (g o f)(0) = g(f(0)) = g(3) = 12 0 f(x) = x 2 + 3 3 g(x) = 4x 12