3

Part of 1995 Italy TST

Problems(1)

Functional inequality condition

Source: Italy TST 1995

f:\mathbb{R}\rightarrow\mathbb{R}

satisfies the conditions \begin{cases}f(x+24)\le f(x)+24\\ f(x+77)\ge f(x)+77\end{cases} \text{for all}\ x\in\mathbb{R} Prove that

f(x+1)=f(x)+1

x

inequalitiesfunctionalgebrafunctional equationalgebra solvedBoundingItaly TST