1. Starter Easy (hopefully) sub values into functions card activity

4. Harder one: A function is defined by : f(x) = (x+3)(x-5) Find the inverse and state the domain and range of f(x) and f -1 (x)

5. A function is defined by : f(x) = (x-16)(x-4) Find the inverse and state the domain and range of f(x) and f -1 (x)

6. Homework: Edpuzzle: Video on combined transformations and complete quiz New class code: ejRZ9Y

7. Functions recap and consolidation  Recap all work on functions.  Go over harder inverse functions, particularly with e x and ln x  Reinforce other harder inverse functions such as quadratics and algebraic fractions

8. Inverse functions Inverse functions only exist for one-one functions.

9. Things to note..  The domain of f -1 is the range of f and the range of f -1 is the domain of f.  The graph of an inverse function can be found by reflecting a function in the line y=x

10. Have a go: Functions and Inverses card match ppt: 10 questions

11. MWB: Inverse functions with e x f(x) = e 2x-1 + 6 x = e 2y-1 + 6 x - 6 = e 2y-1 ln(x - 6) = ln e 2y-1 ln(x - 6) = 2y - 1 The inverse of f(x) is … f -1 (x) = ½(ln(x-6) + 1) Domain ? ln(x - 6) +1 = 2y ½(ln(x - 6) +1) = y Domain is x > 6 Cannot have ln of numbers less than 0

12. MWB: Inverse functions with ln x f(x) = ln(2x) + 6 x = ln(2y) + 6 x - 6 = ln (2y) e x-6 = e ln 2y e x-6 = 2y The inverse of f(x) is … f -1 (x) = ½ e x-6 Domain ? ½ e x-6 = y

13. Have a Go General Functions questions 5 exam questions relay Skip modulus questions ppt: 10 questions

14. Plenary

16. Plenary

26. f(x) = x. x+1 Show that f -1 (x) = 1 - 1 1-x Extension: