7.5 Inverse Function

3/13/2013

x 2x+ 3 x

-2

-1

0

1

-1

1

3

5

-1

1

3

5

-2

-1

0

1

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.

𝒇 (𝒙)=𝟐𝒙+𝟑 𝒚=𝒙

𝒇 −𝟏(𝒙)=𝟏𝟐𝒙+

𝟑  𝟐

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

Inverse FunctionA 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 function is the set of ordered pairs obtained by interchanging the domain(input) and range (output) values in the original function.

a. If then = ?

b. If then = ?

c. If and then = ?

d. Iffind

3

-4

1

5

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

Based on the above definition, answer the following questions.

Steps for finding the inverse of a function:1. Replace f(x) with y.

2. Switch x and y in the original equation.3. Solve for y. Replace y with (1) (2) (3) (3)

Find the inverse of the following functions.

b.) 𝑓 −1(𝑥)=−

32𝑥+9

𝑓 −1(𝑥)=𝑥3

+1