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!

### Conclusion Questions

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

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

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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) = 5x2 – 12 Click on the missing information.

### Pause and Reflect

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

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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. 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

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 f -1(x) x y 6 -8 3 -2 0 4 -3 10 -6 16 2. Find the inverse of the equation f(x) = 2 over 2 2 3 x + 4.

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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 