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7.5 Inverse Function. 3/13/2013. -1 1 3 5. -2 -1 0 1. -2 -1 0 1. -1 1 3 5. What do you notice about the 2 tables (The original function and it’s inverse)?

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7 5 inverse function

7.5 Inverse Function

3/13/2013


-1

1

3

5

-2

-1

0

1

-2

-1

0

1

-1

1

3

5

What do you notice about the 2 tables (The original function and it’s inverse)?

The input of the original function is the output of the inverse and the output of the original function is the input of the inverse.


Notice the graphs of are mirror images of each other along y = x


Inverse function
Inverse Function

A function and its inverse function can be described as the "DO" and the "UNDO" functions.

Inverse function is written as “f inverse of x”

The inverse of a functionis the set of ordered pairs obtained by interchanging the domain(input) and range (output) values in the original function.


The inverse of a functionis the set of ordered pairs obtained by interchanging the domain(input) and range (output) values in the original function.

  • If then = ?

  • If then = ?

  • If and then = ?

  • Iffind

Based on the above definition, answer the following questions.

3

-4

1

5


Steps for finding the inverse of a function
Steps for finding the inverse of a function:

  • Replace f(x) with y.

  • Switch x and y in the original equation.

  • Solve for y. Replace y with

    (1)

    (2)

    (3)

    (3)



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