The function $\mathrm{f}$ is given by $\mathrm{f}:x\mapsto \frac{4{{x}^{2}}-7x-1}{x-2}$, $x\in \math

Question

The function $\mathrm{f}$ is given by $\mathrm{f}:x\mapsto \frac{4{{x}^{2}}-7x-1}{x-2}$, $x\in \mathbb{R},\ x
e 2$. Sketch the graph of $y=\mathrm{f}\left( x ight)$, indicating its turning points and asymptotes. [4] State the range of $\mathrm{f}$. [2] The function $\mathrm{g}$, with domain the set of positive integers, is given by ${\mathrm{g}(n) = \begin{cases} n, & \mathrm{for } n \mathrm{ odd} \ 2\mathrm{g}\left(\frac{n}{2}ight) + 1, & \mathrm{for } n \mathrm{ even} \end{cases}}$ Find $\mathrm{g}\left( 2 ight)$ and $\mathrm{g}\left( 8 ight)$. [2] Does $\mathrm{fg}$ exist? Justify your answer. [2]

Accepted Answer

V.A.: $x = 2$, O.A.: $y = 4x + 1$, $R_f = (-\infty, 5] \cup [13, \infty)$, $g(2) = 3$, $g(8) = 15$

2022 EJC Promo Q10

2022 EJC Promo Q10

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