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StepMaths Mock Paper 2 · Q5

Paper 2Functions & graphs

Claim: For any real function ff and real number xx, if f(f(x))=xf(f(x))=x, then f(x)=f−1(x)f(x)=f^{-1}(x).

Which of the following is a counter example to the above claim?

Af(x)=x ∀x∈R, x=−1f(x)=x\ \forall x\in\R,\ x=-1
Bf(x)=1x ∀x>0, x=1f(x)=\dfrac1x\ \forall x>0,\ x=1
Cf(x)=1x ∀x>0, x=−1f(x)=\dfrac1x\ \forall x>0,\ x=-1
Df(x)=1 ∀x∈R, x=−1f(x)=1\ \forall x\in\R,\ x=-1
Ef(x)=1 ∀x∈R, x=1f(x)=1\ \forall x\in\R,\ x=1

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