Module 2 – Functions
2.4 – Inverse Functions
As time progresses, the hands of a clock move around and they can only
have one position at any given time. So their position is a function of
the time. But when we read the clock we are using the position of the
hands to determine the time rather than using the time to determine the
position. This relation of the time to the observed hand position is in
a sense ‘opposite’ to that of position to time so we refer to these as
inverse relations. Of course, reading the clock tells us the time of
day but not the date, so it doesn’t completely determine the actual
instant of time unless we restrict to a single 12 hour interval. If we
do restrict to a single 12 hour interval, then the time is completely
determined by the hand position, and the function giving time in terms
of position is called the inverse function of the one giving hand
position in terms of time. The use of the word ‘inverse’ in this
context just refers to the reversed direction of the relationship and
has nothing to do with the algebraic inverse which we will from now on
refer to only as the ‘reciprocal’.
What to do
- Use this
'Reading Guide'
link to guide your reading of section 4.1 of the text. As you proceed,
use the questions in the reading guide to confirm your
understanding,keep in mind your
Learning Objectives for this section, and when you have finished be
sure to follow the suggestions regarding Further Practice.
- When you feel that you are ready, go on to do the Assignment for this module.