The Inverse Function Analogy - Disassembling and Reassembling an
Egg Beater
Introduction To MOVIE
The inverse function reverses operations in reverse order. For
example, in the function f(x) = (3x - 5)/2, the operations are:
- Multiply by 3
- Subtract 5
- Divide by 2
To reverse these operations in reverse order, we
- Multiply by 2
- Add 5
- Divide by 3
So the inverse function is f^{ -1}(x) = (2x + 5) / 3.
Repairing a Broken Egg Beater
To repair a broken egg beater, the following steps were performed:
- Remove the cover. This step is denoted C.
- Remove the motor. This step is denoted M.
- Remove the handle. This step is denoted H. (I then
fixed the egg beater by jiggling a loose wire!)
- Reattach the handle. This step is denoted H^{-1}.
(In the movie this was also denoted H^{~}).
- Reattach the motor. This step is denoted M^{-1}.
(In the movie this was also denoted M^{~})
- Reattach the cover. This step is denoted C^{-1}.
(In the movie this was also denoted C^{~})
The total sequence of steps is C*M*H*H^{-1}*M^{-1}*C^{-1}
where the symbol * is only used here to separate the operations.
In this notation, each step followed by it's inverse (reverse)
operation results in a cancellation. So for example, H*H^{-1}
results in the egg beater handle being back in it's original state.
Likewise, M*M^{-1} and C*C^{-1} result
in similar "cancellations".
Watch the MOVIE and
answer the question at the end.
Even though this egg beater repair really
happened as portrayed in the video, the movie cited is for
demonstration purposes only and is not intended as a repair guide.
High voltages of plug-in appliances can be deadly. Repairs of plug in
appliances should only be performed by qualified electricians. |