004 Sample Final A, Problem 1

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Find for

How would you find the inverse for a simpler function like
You would replace with . Then, switch and . Finally, we would solve for .


Step 1:
We start by replacing with .
This leaves us with
Step 2:
Now, we swap and to get .
Step 3:
Starting with , we multiply both sides by to get
Now, we need to get all the terms on one side. So, adding and to both sides we get
Step 4:
Factoring out , we get . Now, dividing by , we get
. Replacing with , we arrive at the final answer
Final Answer:

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