Consider \(f:(-\infty, 1]\rightarrow R, f(x)=x^2-2x\). Part of the graph of \(y=f(x)\) is shown below.
- State the range of \(f\). (1 mark)
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- Sketch the graph of the inverse function \(y=f^{-1}(x)\) on the axes above. Label any endpoints and axial intercepts with their coordinates. (2 marks)
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- Determine the equation of the domain for the inverse function \(f^{-1}\). (2 marks)
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- Calculate the area of the regions enclosed by the curves of \(f,\ f^{-1}\) and \(y=-x\). (2 marks)
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