2021 SJI P1 Q4

2021 SJI P1 Q4

IB Year 5 | Grade 11
8 marks

Let \(\mathrm{g}(x)=x+\sin x,\ -\pi\leq x\leq\pi\).

  1. Find the values of \(x\) for which \(\mathrm{g}'(x)\geq0\).[2]
  2. Hence or otherwise, show that \(\mathrm{g}\) is one-one.[2]
  3. Solve for \(x\) such that \(\mathrm{g}(x)=\mathrm{g}^{-1}(x)\).[4]

Solution:

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Answer:(a) \([-\pi,\pi]\) (b) Strictly increasing, hence one-one. (c) \(x=-\pi,0,\pi\)

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