Properties of Functions (id: d1654348d)

本题目来源于试卷: Properties of Functions，类别为 IB数学

[问答题]
Harry is planning on constructing a glass window in one (hty/ bap-ez2s1*hn 8krdwe:of t)ndf)mh;ibz2m:g k( m he outer walls of his house. The dmm: )m(inkf;bgd2z h)imensions of the wall space available are 2m x 2m. Harry wants the window to be in the shape shown in the diagram below. The bottom section is a rectangle and the top part is a semicircle of radius x m. Harry wants the height of the rectangle to be fixed at 1 m.



1. Write down a function P (in metres) for the perimeter of the window in terms of the radius, x .
2. Determine the domain and range of P , taking into consideration the dimensions of the available wall.
3. Find an equation for the inverse function $P^{-1}(x)$ .

Harry wants to maximise the size of the window, however the window frame that covers the perimeter of the window can only be 5,6 , or 7 metres long, due to manufacturing restrictions.
4. Determine which perimeter length is the best option for Harry.

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