1. 4.1 Inverses Mon March 23 Do Now Solve for Y 1) 2)

2. Quiz Review Retakes?

3. Inverses When we go from an output of a function back to its inputs, we get an inverse relation Interchanging the first and second coordinates of each ordered pair produces the inverse relation

4. Notation The notation for the inverse of f(x) is This is not an exponent!

5. One-to-one Functions A function f is one-to-one if different inputs have different outputs If Every y-value is unique

6. Properties of one-to-one functions If a function f is one-to-one, its inverse is a function The domain of a one-to-one function f is the range of its inverse The range of a one-to-one function is the domain of its inverse A function that is always increasing or decreasing is one-to-one

7. Ways to show a function is one-to-one 1) Assume f(a) = f(b); then show that a = b – If you can think of a y-value that has 2 x-values (ex: x^2 2) Horizontal Line Test – If a horizontal line intersects the graph more than once, it is NOT one-to-one

8. How to find a formula for inverse 1) Replace f(x) with y (if possible) 2) Switch x and y 3) Solve for y 4) Replace y with

9. Ex Find an equation for the inverse of the relation

10. Ex2 Find an inverse for the function

11. You try Find an inverse for the following 1) f(x) = 7 - x 2) 3)

12. Closure Find the inverse for the function HW: p.356 #17-59 odds

13. 4.1 Inverses and Compositions Tues March 24 Do Now Find the inverse of

14. HW Review: p.356 #17-59 odds

15. Inverses and Graphs The graph of an inverse function is a reflection of f(x)’s graph across the line y = x

16. Inverse Functions and Compositions If a function f(x) is one-to-one, then the following compositions are true: for each x in the domain of f for each x in the domain of f inverse

17. Ex Given f(x) = 5x + 8, find its inverse and show they are inverses using composition

18. Ex Given, find its inverse and show they are inverses using composition

19. Restricting the domain In the case in which the inverse of a function is not a function, the domain can be restricted to allow the inverse to be a function This is why square root graphs only show half of the true graph in a calculator

20. Closure Find the inverse of and show they are inverses using compositions HW: p.358 #67-87 odds