MathDB

3

Part of 1999 Italy TST

Problems(1)

Function doesn't exist when power of y is > 1

Source: Italy TST 1999

2/1/2011
(a) Find all strictly monotone functions f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} such that f(x+f(y))=f(x)+y \text{for all real}\ x,y. (b) If n>1n>1 is an integer, prove that there is no strictly monotone function f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} such that f(x+f(y))=f(x)+y^n  \text{for all real}\ x, y.
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