Question:
Find two functions f,g: R -> R such that neither f nor g is a constant map, but g o f is a constant map.
Attempt:
I know for something to be a constant map graphically it means the function is a horizontal line. However, I am having trouble coming up with two functions whose composition is a constant map but they themselves are not a constant map.
Would appreciate any input or hint in the right direction.
I don't mean to disappoint you, but there was no real thought process there/
Look at this thread. I just happened to have been thinking about those functions.
That's very convenient. Anyways thanks your functions work well for my example. Out of curiosity I seem to be overlooking how these functions are sufficient to disprove the claim posted by the user in the other thread.
For instance, for x0 = 1 we have the limit equal different values, but the claim said "if the limits are the same for any real value of x0".
Edit: I take that back the functions do work. The cause of the confusion on my part (and perhaps the other person) was that you made a typo for f(x) in post 2 of the linked thread.