IB MAI HL Functions Topic 2.3 Properties of Functions (id: 1f29cebdf)

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]
Consider the followind/21kmhoio2z o* v,f eg composite shape, coye0j8mz;m e -dnsisting of a rectangle of length 50 cm and varying width x cm, and three-quarter circle with its center at a vertex of the rectangle and radius equal to the rectangle widmee;ym8dj0z -th, x cm.



1.Determine a function, L, in terms of x, for the total length of line seen in the diagram. This consists of both the perimeter of the rectangle and circumference of the three-quarter circle.2
Constraints are placed on the dimensions of the composite shape. The total length and width of the composite shape cannot exceed 100 cm and 80 cm respectively.
2.Determine the domain and range of L, taking into consideration these constraints.
3.Find an equation for the inverse function $L^{−1}(x)$. Express your answer in the form $L^{−1}$(x)=mx+c.
Suppose L can only be in multiples of 100 cm (i.e., 100 cm, 200 cm, 300 cm, ...).
4.Determine the maximum length of L that satisfies the constraints.

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