Investigation+3D+Inverse

Target 3D: Create the inverse of a function (table and graph)
Return Trip

Suppose you are given the following directions from Google Maps: 1. From Naperville Central High School travel east on Aurora Avenue for 0.5 miles. 2. Turn right (south) on Washington Street and travel for 2.0 miles. 3. Turn left (east) on 75th Street and travel for 0.8 miles. 4. Turn right (south) on Naper Boulevard and travel 1.0 miles. 5. Turn left (east) on River Oak Drive and travel 0.4 miles. 6. Madison Junior High will be on your right.

If you start from Madison Junior High, what will the return trip directions to Naperville Central be? 1. 2. 3. 4. 5. 6.

Suppose you are given the following algorithm:
 * 1) Starting with a number, add 5 to it
 * 2) Divide the result by 3
 * 3) Subtract 4 from that quantity
 * 4) Double your result The final result is 10.

Working backwards knowing this result, find the original number. Show your work.

Write a function f(x), which when given a number x (the original number) will model the operations given above. Click here for the answer

Write a function g(x), which when given a number x (the final result), will model the backward algorithm that you came up with above. Click here for the answer

The function g(x) is like the return trip to the high school and the decoding cipher from the code breaking in Investigation 3A. This working backwards is called an inverse function.