I’m currently writing a multiple choice placement test for engineering calculus students. I wrote a draft, and sent it in to the professor I’m working for, where he found an error in this question.

Which statement is correct about the f(x) and its inverse, g(x)?

1. g(x) is the reciprocal of f(x)
2. An output so that g(x) = – f(x)
3. g(f(x)) = x
4. g(x) undoes the action of f(x)
5. 3 and 4
6. I don’t know

Have you spotted the problem?

In the question, #3 is right, #4 is right and so is #5. Or is it? The choice #5 doesn’t say that it itself is right. #5 needs to state this fact, given that it isn’t talking about statements about calculus, it is talking about statements which may or may not be true.

I’m reading too much Godel Escher Bach.