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Unformatted text preview: teps that can on occasion be somewhat messy. Here is the process
Finding the Inverse of a Function
Given the function f ( x ) we want to find the inverse function, f -1 ( x ) .
1. First, replace f ( x ) with y. This is done to make the rest of the process easier.
2. Replace every x with a y and replace every y with an x.
3. Solve the equation from Step 2 for y. This is the step where mistakes are most often
made so be careful with this step.
4. Replace y with f -1 ( x ) . In other words, we’ve managed to find the inverse at this point!
5. Verify your work by checking that ( f o f ) ( x ) = x and ( f
-1 -1 o f ) ( x ) = x are both true. This work can sometimes be messy making it easy to make mistakes so again be
That’s the process. Most of the steps are not all that bad but as mentioned in the process there are
a couple of steps that we really need to be careful with.
In verification step we technically really do need to check that both (f -1 ( f o f ) ( x ) = x and
-1 o f ) ( x ) = x are true. For all the functions that we a...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12