004 Sample Final A, Problem 1

From Math Wiki
Jump to navigation Jump to search

Find for

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


Solution:

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:

Return to Sample Exam