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

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

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.

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

Find Inverse of f(x)= x y = x (Swap variables) x = y y 2 = x – 4 y = ± Don’t forget the (±) when taking a square root

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

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

Domain and Range

Graph

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.

Solve

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)

Example 1

Solve