2020 SJI P1 Q2

2020 SJI P1 Q2

IB Year 5 | Grade 11
4 marks

A function \(\mathrm{f}\) is defined by

\[\mathrm{f}(x)=x^2+x,\quad x\leq-\frac12.\]

  1. Find an expression for \(\mathrm{f}^{-1}\).[3]
  2. Find the range of \(\mathrm{f}^{-1}\).[1]

Solution:

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Answer:(a) \(\mathrm{f}^{-1}(x)=-\dfrac12-\sqrt{x+\dfrac14}\), \(x\geq-\dfrac14\) (b) \(\left(-\infty,-\dfrac12\right]\)

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