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tmua.me Medium Set B Paper 2 · Q18

Paper 2Logic & proofFunctions & graphs

A real-valued function ff, defined for every real number, satisfies

f(x)+f(x+1)=2x+1f(x)+f(x+1)=2x+1

for every real xx.

Consider the statements

  • I. f(x+2)=f(x)+2f(x+2)=f(x)+2 for every real xx.
  • II. The values of ff have no real upper bound.
  • III. If a<ba<b, then f(a)<f(b)f(a)<f(b).

Which statements must be true?

AI only
BII only
CI and II only
DI and III only
EII and III only
FI, II and III

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