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- The diagram shows part of the curve \(y = 11 - x ^ { 2 }\) and part of the straight line \(y = 5 - x\) meeting at the point \(A ( p , q )\), where \(p\) and \(q\) are positive constants. Find the values of \(p\) and \(q\).
- The function f is defined for the domain \(x \geqslant 0\) by
$$f ( x ) = \begin{cases} 11 - x ^ { 2 } & \text { for } 0 \leqslant x \leqslant p
5 - x & \text { for } x > p \end{cases}$$
Express \(\mathrm { f } ^ { - 1 } ( x )\) in a similar way.