IB MAI HL Functions Topic 2.3 Properties of Functions (id: 19f97769c)

本题目来源于试卷: IB MAI HL Functions Topic 2.3 Properties of Functions，类别为 IB数学

[问答题]
Harry is planning on constructing a glass win5fb1ekjg di1 n7;8cqi dobkt;8j *q bx:lt 37hemw in one of the outer walls of his house. The dimensions 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. Harry8*7xht3 :jkb;etl mbq 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). Express your answer in the form $P^{−1}$(x)=mx+c.
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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