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.


Interactive exercise. Assistance may be required. Below is a function. Move the given values into the table to create an inverse function.

You just created the inverse of the table!

Conclusion Questions

  1. Determine the inverse, f -1(x), of the coordinate (-2, -8) from the first table.

    Interactive popup. Assistance may be required.

    Check Your Answer

    (-8, -2)Close Pop Up

  2. Describe the difference between the first table and the second table.

    Interactive popup. Assistance may be required.

    Check Your Answer

    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. Close Pop Up

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) = 5x2 – 12

Interactive exercise. Assistance may be required. Click on the missing information.

Pause and Reflect

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

Interactive popup. Assistance may be required.

Check Your Answer

For a table, the x-values of the function are the y-values of its inverse, and the y-values of the function are the x-values of its inverse. When you find the inverse of an equation, the x- and y-values are also exchanged except the equation is solved for y. Close Pop Up

  1. Create a table showing the inverse of the given table.
    f(x)
    x
    y
    -8
    6
    -2
    3
    4
    0
    10
    -3
    16
    -6

    Interactive popup. Assistance may be required.

    Check Your Answer

    f -1(x)
    x
    y
    6
    -8
    3
    -2
    0
    4
    -3
    10
    -6
    16
    Close Pop Up

  2. Find the inverse of the equation f(x) = 2 over 2 2 3 x + 4.

    Interactive popup. Assistance may be required.

    Check Your Answer

    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
    3x – 12 = 2y
    3x - 12 over 2 3x – 12 2 = 2 over 2 2 2 y
    3x - 12 over 2 3x – 12 2 = y
    3x over 2 3x 2 – 6 = y
    f -1(x) = 3x over 2 3x 2 − 6 Close Pop Up