TMUA Official 2017 Paper 2 · Question 16

Official papers

Official 2017 Paper 2 · Q16

Paper 2Logic & proofNumber & counting

Consider the following statement:

$(*)$ If $f(x)$ is an integer for every integer $x$ , then $f'(x)$ is an integer for every integer $x$ .

Which one of the following is a counterexample to $(*)$ ?

f(x)=\frac{x^3+x+1}4

f(x)=\frac{x^4+x^2+x}2

f(x)=\frac{x^4+x^3+x^2+x}2

f(x)=\frac{x^4+2x^3+x^2}4

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