Functions and Inverses

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Presentation transcript:

Functions and Inverses

Inverses An INVERSE RELATION “undoes” the relation. The Inverse of f(x) is denoted by f-1(x)

Inverse So if f(x) = x – 5 Then f-1(x) = x + 5

Domains and Ranges The domain of a relation’s inverse is its range, and the range of a relation’s inverse is its domain. f(x): D R f-1(x): D R -1 2 6 7 -1 2 6 7 1 2 4 1 2 4

More Inverse Find the inverse of the following relation: {(2,3), (4,5), (1,3)}

Try some! Find the inverse of the following relations: {(3,4), (-4, -6), (-3, 2), (6, -1)} {(2, 5), (1, 5), (3, 5)}

Functionality of Inverses If a relation is a function, does it’s inverse have to be??

How to find the inverse of a function: Switch the x and y, and solve for y. Ex: y = 5x - 15

Find the inverse: Ex: y = 6 – 2x

You Try! Find the Inverse of the following: y = x – 5 y = 2x + 10

Function Inverse Exit Ticket Find the inverse of the following functions: 1. y = 3(x + 2) 2. y = 3x + 4x – 2 3. y = 2x + 6 4. y = 3x – 6 5. y = 6 – x 6. y = x 7. y = x + 4 8. y = -x + 3