1. Composition of Functions

2. Remember … A composition of functions means a function of a function.  Work out 1st function.  Plug the answer into the 2nd function.

4. Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f (7) f  g (2) f  f (3)

5. Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f (7)
Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f (7) 2  = 102 f  g (2) 82 = 64 f  f (3) 92 = 81

6. Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f  g  f (5)

7. Suppose f(x) = x2 and g(x) = 2x + 4
Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f  g  f (5) = g  f  g(25) = g  f(54) = g(2916) = 5,836

8. What is g  f (3) ? g  f (1) ?

9. What is g  f (3) = y g  f (1) = z

10. Find the domain and range of g  f

11. DOMAIN { 1, 2, 3 }

12. RANGE { x, y, z }

13. _____ If g(x) =  x – 3 and f(x) = x3 Find the domain and range of f  g(x)

14. _____ If g(x) =  x – 3 and f(x) = x3 DOMAIN … x – 3 > 0,
_____ If g(x) =  x – 3 and f(x) = x3 DOMAIN … x – 3 > 0, so x > 3

15. _____ If g(x) =  x – 3 and f(x) = x3 RANGE … The answers from g will always be positive, so the answer cubed will be positive too … y > 0