# function with different image, smae preimage

• October 9th 2009, 08:07 PM
altave86
function with different image, smae preimage
Please give an example of a function f, and two sets $U_1,U_2:U_1 \subset U_2, U_1 \neq U_2$ but $f^{-1} (U_1)=f^{-1}(U_2)$?

Is there such a function in $R^n$?
• October 10th 2009, 06:49 AM
HallsofIvy
Define f to map all of $R^n$ to a single point. The inverse image of any set containing that point is all of $R^n$.