In fact, it is one of the ways in which I introduce finding the
formula for the inverse of certain functions.
For example, given f(x) = 5x + 1, this says that to find the value of
f(x), start with x, multiply by 5, then add 1 to the result.
Since the inverse of a function "takes a value back from whence it
came" we want to undo the above.
To undo
start with x, multiply by 5, then add 1 to the result,
take the result, and
subtract 1, then divide this by 5. (read the line above from
right to left).
Therefore the inverse function is
f-1(x) = (x - 1)/5
This works well for linear functions, and I don't try to go further
with it. But it's another way to view the inverse of a function.
Phil Mahler
Middlesex CC
Bedford, MA