- #1
lordianed
- 23
- 7
Homework Statement
Prove that there do not exist functions ##f## and ##g## with the following property:
$$(\forall x)(\forall y)(f(x+y) = g(x) - y)$$
Homework Equations
NA
The Attempt at a Solution
Here is some information I have found out about ##f## and ##g## if we suppose they exist:
##f(x +0) = f(x) = g(x) = g(x)-0## for all x, so ##f## and ##g## are equal. Hence, ##f(x+y) = f(x) - y## for all ##x## and ##y##. Thus, ##f(y) = f(0) - y##, so ##f## is a linear function. Any suggestions as to what kind of values I have to substitute to arrive at a contradiction from here on? Thanks!