5 The function f is defined by \(\mathrm { f } ( x ) = \frac { 2 x + 1 } { 2 x - 1 }\) for \(x < \frac { 1 } { 2 }\).
- State the value of \(\mathrm { f } ( - 1 )\).
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The diagram shows the graph of \(y = \mathrm { f } ( x )\). Sketch the graph of \(y = \mathrm { f } ^ { - 1 } ( x )\) on this diagram. Show any relevant mirror line.- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of the function \(\mathrm { f } ^ { - 1 }\).
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The function g is defined by \(\mathrm { g } ( x ) = 3 x + 2\) for \(x \in \mathbb { R }\).
- Solve the equation \(\mathrm { f } ( x ) = \mathrm { gf } \left( \frac { 1 } { 4 } \right)\).
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The diagram shows a metal plate \(O A B C D E F\) consisting of sectors of two circles,each with centre \(O\) . The radii of sectors \(A O B\) and \(E O F\) are \(r \mathrm {~cm}\) and the radius of sector \(C O D\) is \(2 r \mathrm {~cm}\) . Angle \(A O B =\) angle \(E O F = \theta\) radians and angle \(C O D = 2 \theta\) radians.
It is given that the perimeter of the plate is 14 cm and the area of the plate is \(10 \mathrm {~cm} ^ { 2 }\) .
Given that \(r > \frac { 3 } { 2 }\) and \(\theta < \frac { 3 } { 4 }\) ,find the values of \(r\) and \(\theta\) .
| ΝΙ১W SΙΗ ΝΙ ΞΙΙΥΜ ΙΟΝ Ο0 | ΝΙ১W SIH NI IyM 1ON OO | ΝΙ১W SΙΗΙ ΝΙ ΞΙΙΨΜ ΙΟΝ Ο0 | ΝΙ১W SIHI NI IYM 1ON OC | \includegraphics[max width=\textwidth, alt={}]{39393c20-34df-4167-a8bf-e4067371de81-08_437_28_2390_2016} |