examday

Official papers

Official 2021 Paper 2 · Q17

Paper 2Logic & proofPowers & logarithms

Consider the following functions defined for x>1x>1:

f(x)=log⁡2 ⁣(log⁡2x)f(x)=\log_2\!\left(\log_2\sqrt{x}\right)
g(x)=log⁡2 ⁣(log⁡2x).g(x)=\log_2\!\left(\sqrt{\log_2x}\right).

Which one of the following is true for all values of x>1x>1?

A0≤f(x)≤g(x)0\le f(x)\le g(x) or g(x)≤f(x)≤0g(x)\le f(x)\le0
B0≤g(x)≤f(x)0\le g(x)\le f(x) or f(x)≤g(x)≤0f(x)\le g(x)\le0
C12≤f(x)≤g(x)\frac12\le f(x)\le g(x) or g(x)≤f(x)≤12g(x)\le f(x)\le\frac12
D12≤g(x)≤f(x)\frac12\le g(x)\le f(x) or f(x)≤g(x)≤12f(x)\le g(x)\le\frac12
E1≤f(x)≤g(x)1\le f(x)\le g(x) or g(x)≤f(x)≤1g(x)\le f(x)\le1
F1≤g(x)≤f(x)1\le g(x)\le f(x) or f(x)≤g(x)≤1f(x)\le g(x)\le1

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →