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

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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.

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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

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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

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

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

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Domain and Range

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Graph

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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.

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Solve

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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)

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Example 1

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Solve

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