Final Exam Review Pages 4-6

1. Final Exam ReviewPages 4-6 Inverses Solving Radical Equations Solving Radical Inequalities Square Root (Domain/Range)

2. Inverse Concept • The main concept of an inverse is the x and y coordinates have switched places

3. FINDING A FORMULA FORAN INVERSE FUNCTION • Replace f (x) with y. • Interchange x and y. • Solve the resulting equation for y. • Replace y with f-1(x) if the inverse is a function.

4. y = Solve for y. Example: Inverse Relation Algebraically To find the inverse of a relation algebraically, interchange x and y and solve for y. Example:Find the inverse relation algebraically for the function f(x) = 7x+ 4. y = 7x+ 4Original equation defining f x = 7y+ 4Switch x and y. 7y+ 4 =xReverse sides of the equation.

5. Find Inverse of f(x)= x2 + 4 • y = x2 + 4 (Swap variables) • x = y2 + 4 • y2 = x – 4 • y = ± • Don’t forget the (±) when taking a square root

6. Domain & Range What’s under the radical determines starting point of the DOMAIN What’s after the radical determines starting point of the RANGE

7. Domain & Range Domain: [-1, ∞) Range: [3, ∞)

8. Domain and Range

9. Graph

10. y-axis 9 8 7 6 5 4 3 2 10 -9 -8 -7 -6 -2 1 0 -5 -4 -3 -1 x-axis 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9

11. Solving Radical Equations • When solving radical equations make sure only the radical is on the left when you start the problem. • To UNDO a radical, you take it to the POWER of the Index Number • ALWAYS Check answers. You may get Extraneous Solutions from radicals.

12. Solve

13. Solve

14. Solve

15. Solving Radical Inequalities • MUST put radical expression on left of inequality into graphing calculator as y1 = • MUST put radical expression on right of inequality into graphing calculator as y2= • Graph the equation • Then find INTERSECTION (2nd, TRACE, #5)

16. Example 1

17. Solve

18. Solve