It’s a long weekend here. Too nice to do Calculus. Let’s do pre-calculus instead.
Example: Express in terms of .
The textbook (in its 13th edition) proceeds thus.
. Here we have assumed that . Although is defined for , the expressions is defined only if . Note that we do have for all .
This leaves me doubly confused. Which of two answers is a student supposed to give? And what does “express A in terms of B” really mean?
Concerning the latter, I can only suppose it means: exhibit a function such that (using the composition notation, since and are functions themselves). With this interpretation, the correct answer should be: it is impossible to express in terms of .