Methods2023 Exam 1 · Q7Tech-free7 marks

Inverse of a restricted quadratic and enclosed area

Consider $f: (-\infty, 1] \to \R, f(x) = x^2 - 2x$ . Part of the graph of 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 and 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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