[问答题]
Harry is planning on constructing a
3 or,g efqb;*t,l: mk 8)5,ti akehnlpglass window in one of
ph 0 f x0.uj3 2mor94h7 0qzdoxqbbes6the outer walls of his hou
bzxo 3hjq .p df40ub o2rqhm06sx07e9 se. 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. 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.
