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Final Exam Review Pages 4-6  Inverses  Solving Radical Equations  Solving Radical Inequalities  Square Root (Domain/Range)

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Presentation on theme: "Final Exam Review Pages 4-6  Inverses  Solving Radical Equations  Solving Radical Inequalities  Square Root (Domain/Range)"— Presentation transcript:

1 Final Exam Review Pages 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 FOR AN INVERSE FUNCTION 1. Replace f (x) with y. 2. Interchange x and y. 3. Solve the resulting equation for y. 4. Replace y with f -1 (x) if the inverse is a function.

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

5 Find Inverse of f(x)= x 2 + 4 y = x 2 + 4 (Swap variables) x = y 2 + 4 y 2 = 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

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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

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15 Solving Radical Inequalities MUST put radical expression on left of inequality into graphing calculator as y 1 = MUST put radical expression on right of inequality into graphing calculator as y 2 = Graph the equation Then find INTERSECTION (2 nd, TRACE, #5)

16 Example 1

17 Solve

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