The function $\mathrm{f}$ is defined as follows. $\mathrm{f}:x\ \ \mapsto (2x-1)(2x+3),\mathrm{ }x\i

Question

The function $\mathrm{f}$ is defined as follows. $\mathrm{f}:x\ \ \mapsto (2x-1)(2x+3),\mathrm{ }x\in \mathbb{R},\ x\le -\frac{1}{2}$. Find the range of f and define ${{\mathrm{f}}^{-\mathrm{1}}}$ in a similar form. [4] Given that ${{\mathrm{f}}^{-1}}\left( x \right)=\mathrm{f}\left( x \right)$ at $x=a$, find the exact value of $a$. [3]

Accepted Answer

(i) $R_{\mathrm{f}} = [-4, \infty)$; $\mathrm{f}^{-1}: x \mapsto -\frac{1}{2} - \frac{\sqrt{x+4}}{2},\ x \ge -4$ (ii) $a = \frac{-3-\sqrt{57}}{8}$

2013 ACJC P1 Q7

2013 ACJC P1 Q7

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