Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
one-to-one functions?
Prove the following assertion or give a counterexample. Given any set x and any functions f, g, and h mapping x to x, if h is one-to-one and f º h = g º h then f = g.
Please help I am having a lot of trouble...thanks!
2 Answers
- iluxaLv 51 decade agoFavourite answer
Disproving.
Idea is this: since h may no be onto, there's no telling how f and g will behave for values which h does not produce.
Counter-example: take
x = real numbers,
h(x) = e^x
f(x) = x
g(x) = |x|
f º h = f(h(x)) = f(e^x) = e^x
g º h = g(h(x)) = g(e^x) = |e^x| = (since e^x > 0 for any x) e^x
yet f is not equal to g.
- Anonymous1 decade ago
Well since the question says "prove" that is true it can't be false. If the statement were false it would have said prove or disprove.