SOLUTION: Suppose that v(t) = 10^t-1 +2 Compute v^-1 (t)

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Question 89238: Suppose that v(t) = 10^t-1 +2 Compute v^-1 (t)
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose that v%28t%29 = 10%5E%28t-1%29%2B2 
Compute v%5E%28-1%29%28t%29

The 4 steps for finding the inverse of a function are: 

1. Replace v%28t%29 by y
2. Interchange the two variables
3. Solve for y
4. Replace y by v%5E%28-1%29%28t%29

======================================

v%28t%29 = 10%5E%28t-1%29%2B2

1. Replace v%28t%29 by y

   y = 10%5E%28t-1%29%2B2

2. Interchange the two variables

   t = 10%5E%28y-1%29%2B2

3. Solve for y

   Subtract 2 from both sides:

t-2 = 10%5E%28y-1%29

   Take logs of both sides:

log%28%28t-2%29%29 = y-1

   Add 1 to both sides:

1%2Blog%28%28t-2%29%29 = y

   Swap sides:

y = 1%2Blog%28%28t-2%29%29

4. Replace y by v%5E%28-1%29%28t%29

v%5E%28-1%29%28t%29 = 1%2Blog%28%28t-2%29%29

Edwin