CAIE P1 2015 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionJune
TopicComposite & Inverse Functions

6
1
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  1. Show that angle \(A B C\) is \(90 ^ { \circ }\).
  2. Find the area of triangle \(A B C\), giving your answer correct to 1 decimal place. 6
    \includegraphics[max width=\textwidth, alt={}, center]{8da9e73a-3126-471b-b904-25e3c156f6bf-2_519_670_1640_735} The diagram shows the graph of \(y = \mathrm { f } ^ { - 1 } ( x )\), where \(\mathrm { f } ^ { - 1 }\) is defined by \(\mathrm { f } ^ { - 1 } ( x ) = \frac { 1 - 5 x } { 2 x }\) for \(0 < x \leqslant 2\).
  3. Find an expression for \(\mathrm { f } ( x )\) and state the domain of f .
  4. The function g is defined by \(\mathrm { g } ( x ) = \frac { 1 } { x }\) for \(x \geqslant 1\). Find an expression for \(\mathrm { f } ^ { - 1 } \mathrm {~g} ( x )\), giving your answer in the form \(a x + b\), where \(a\) and \(b\) are constants to be found.