In the previous section, you learned the definition of the inverse of a function is all ordered pairs (*y*, *x*) where the function itself is the set of all ordered pairs (*x*, *y*). Now you are going to observe and practice inverses of functions represented by tables in order to better understand the definition.

Below is a function. Move the given values into the table to create an inverse function.

You just created the inverse of the table!

- Determine the inverse,
*f*^{-1}(*x*), of the coordinate (-2, -8) from the first table.Interactive popup. Assistance may be required.

(-8, -2) - Describe the difference between the first table and the second table.
Interactive popup. Assistance may be required.

The*x*-values of the first table are the*y*-values of the second table, and the*y*-values of the first table are the*x*-values of the second table.

If you are given an **equation**, the process is very similar; always remember an inverse of the function is the exchange of the *x*- and *y*-values.

Find the inverse of the equation: *f*(*x*) = 5*x*^{2} – 12

Click on the missing information.

Compare and contrast finding the inverse of a table vs. finding the inverse of an equation.

Interactive popup. Assistance may be required.

For a table, the-
Create a table showing the inverse of the given table.
**f****(***x*)**x****y**-86-234010-316-6Interactive popup. Assistance may be required.

**f**^{-1}(*x*)**x****y**6-83-204-310-616 - Find the inverse of the equation
*f*(*x*) = 2 over 2 2 3*x*+ 4.Interactive popup. Assistance may be required.

*f*(*x*) = 2 over 3 2 3*x*+ 4

*y*= 2 over 3 2 3*x*+ 4

*x*= 2 over 3 2 3*y*+ 4

*x*− 4 = 2 over 3 2 3*y*+ 4 − 4

*x*− 4 = 2 over 3 2 3*y*

3(*x*– 4) = 3(2 over 3 2 3 )*y*

3*x*– 12 = 2*y*

3x - 12 over 2 3*x*– 12 2 = 2 over 2 2 2*y*

3x - 12 over 2 3*x*– 12 2 =*y*

3x over 2 3*x*2 – 6 =*y*

*f*^{-1}(*x*) = 3x over 2 3*x*2 − 6