1. Finding Inverses (thru algebra) & Proving Inverses (thru composition) MM2A5b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = x a, including the use of restricted domains. MM2A5d. Use composition to verify that functions are inverses of each other.

2. Finding Inverses of Functions usingALGEBRA!!

3. To find the inverse of a function: 1. Change the f(x) to a y. 2. Switch the x & y values. 3. Solve the new equation for y. ** Remember functions have to pass the vertical line test!

4. Example 1: Find the inverse of f(x) = -3x + 6.  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

5. Example 2: Find the inverse of f(x) = x 2 - 5.  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

6. Example 3: Find the inverse of f(x) = x 3 - 4.  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

7. Example 4: Find the inverse of f(x) =.  Steps: -change f(x) to y -switch x & y -solve for y -solve for y

8. You Try!! 1) Find the inverse of f(x) = 2x - 1.

9. You Try!! 2) Find the inverse of f(x) = 2x 2 - 6.

10. You Try!! 3) Find the inverse of f(x) =.

11. You Try!! 4) Find the inverse of f(x) =.

12. Proving Functions are Inverses usingCOMPOSITION!!

13. Inverse Functions  Given 2 functions, f(x) & g(x), if f(g(x)) = x AND g(f(x)) = x, then f(x) & g(x) are inverses of each other. Remember: Remember: f -1 (x) means “f inverse of x”

14. Example 1: Verify that f(x) = -3x+6 and g(x) = -1 / 3 x+2 are inverses.  Steps:- Find f(g(x)) and g(f(x)). - If they both equal x, then they are inverses.

15. Example 2: Verify that f(x) = x 2 + 6 and g(x) = are inverses.  Steps:- Find f(g(x)) and g(f(x)). - If they both equal x, then they are inverses.

16. You Try!! 1) Verify that f(x) = 3x - 4 and g(x) = are inverses.

17. You Try!! 2) Verify that f(x) = and g(x) = x 2 - 4 are inverses.

18. You Try!! 4) Verify that f(x) = and g(x) = are inverses.