Inverse Functions and Relations

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Presentation transcript:

Inverse Functions and Relations Lesson 7.2 Inverse Functions and Relations

pg 2 Inverse Relations Two relations are inverse relations if and only if one relation contains the element (a, b) the other relation contains the element (b, a) Example: Q and S are inverse relations Q = {(1, 2), (3, 4), (5, 6)} S = {(2, 1), (4, 3), (6, 5)}

Examples 1. Find the inverse relation of {(2,1), (5,1), (2,-4)} pg 2 Examples 1. Find the inverse relation of {(2,1), (5,1), (2,-4)} 2. Find the inverse relation of {(-8,-3), (-8,-6), (-3,-6)}

Property of Inverse Functions pg 2 Property of Inverse Functions Suppose f and f-1 are inverse functions. Then f(a) = b if and only if f -1 (b) = a To find the inverse of a function: 1. Replace f(x) with y 2. Switch x and y 3. Solve for y 4. Replace y with f-1(x) 5. Graph f(x) and f-1(x) on the same coordinate plane

To Graph a function and it’s inverse pg 2 To Graph a function and it’s inverse 1. Make an x/y chart for f(x) then graph the points and connect the dots 2. Make an x/y chart for f-1(x) by switching the x and y coordinates and then graph and connect the dots - The graphs should be reflections of one another over the line y=x

Examples 3. Find the inverse of and then graph the function and its inverse pg 3

pg 3 4. Find the inverse of and then graph the function and its inverse f(x) = 2x - 3

pg 3 Inverse Functions Two functions f and g are inverse functions if and only if both of their compositions are the identity function. [f o g](x) = x and [g o f](x) = x

5. Determine if the functions are inverses pg 3 5. Determine if the functions are inverses

6. Determine if the functions are inverses pg 3 6. Determine if the functions are inverses