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Omni-MATH / Let f:R→R be a function such that (i) For all x,y∈R, f(x)+f(y)+1≥f(x+y)≥f(x)+f(y) (ii) For all x∈[0,1),f(0)≥f(x), (iii) −f(−1)=f(1)=1. Find all such functions f. · Discussion

Discussing Let f:R→R be a function such that (i) For all x,y∈R, f(x)+f(y)+1≥f(x+y)≥f(x)+f(y) (ii) For all x∈[0,1),f(0)≥f(x), (iii) −f(−1)=f(1)=1. Find all such functions f. · Omni-MATH

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