2017 NJC Promo Q7
2017 NJC Promo Q7
10 marks
Promo
The functions \(\mathrm{f}\) and \(\mathrm{g}\) are defined as
\(\mathrm{f}:x\mapsto \frac{3x}{2x-5},\) for \(-5 < x\le 5\), \(x\ne \frac{5}{2}\)
\(\mathrm{g}\left( x \right)=\left\{ \begin{matrix} 8x-{{x}^{2}}-15,\mathrm{ for }3\le x<4. \\ \frac{5-x}{2},\mathrm{ for }4\le x<6. \\ \end{matrix} \right.\)
- Find \({{\mathrm{f}}^{-1}}\), stating its domain and range.[4]
- Find the value of \(\mathrm{g}\left( 4 \right)\).[1]
- Sketch the graph of \(y=\mathrm{g}\left( x \right)\).[2]
- Show that the composite function \(\mathrm{fg}\) exists and find the range of \(\mathrm{fg}\).[3]
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Answer:\(f^{-1}: x \mapsto \dfrac{5x}{2x-3}\), \(g(4) = \dfrac{1}{2}\), \(R_{fg} = \left(-1, \dfrac{1}{4}\right)\)
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