## Exam-Style Question on Functions## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 469. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

The circumference of a given circle \(C\) can be represented by the function \(C(A) = 2 \sqrt{A \pi}\) , \(A \ge 0 \) , where \(A\) is the area of the circle. The graph of the function \(C\) is shown for \(0 \le A \le 10\).

(a) Write down the value of \(C(5)\).

The range of \(C(A)\) is \(0 \le C(A) \le k\).

(b) Find the value of \(k\).

(c) On the axes above, draw the graph of the inverse function, \( C^{-1}\).

(d) In the context of the question, explain the meaning of \( C^{-1}(10) \approx 7.96\).

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