tmua.fyi Mock Paper 2 · Question 5

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tmua.fyi Mock Paper 2 · Q5

Paper 2Logic & proofFunctions & graphs

$f$ is a function defined for all real numbers, with $f(1)=3$ and $f(4)=-2$ . Consider the statements:

I: $f(x)=0$ has a solution with $1<x<4$ ;

II: $f(x)=0$ has an odd number of solutions with $1<x<4$ ;

III: $f$ takes the value $1$ somewhere in $1<x<4$ .

Which of these must be true?

Anone of them

BI only

CI and II only

DI and III only

EI, II and III

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