008A Sample Final A, Question 1

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Question: Find for

1) How would you find the inverse for a simpler function like ?
2) How do you remove the in the following equation:
1) you would replace f(x) by y, switch x and y, and finally solve for y.
2) By the definition of when we write the equation we mean y is the number such that


Step 1:  
We start by replacing f(x) with y.
This leaves us with
Step 2:  
Now we swap x and y to get
In the next step we will solve for y.
Step 3:  
From , we add 1 to both sides to get
Now we will use the relation in Foundations 2) to swap the log for an exponential to get
Step 4:  
After subtracting 3 from both sides we get . Replacing y with we arrive at the final answer that
Final Answer:  

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