The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{2x-1}{2x-2},\quad xDefine ${{\mat

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{2x-1}{2x-2},\quad xDefine ${{\mathrm{f}}^{-1}}$ in a similar form. Hence or otherwise find ${{\mathrm{f}}^{2}}(x)$ and state the value of ${{\mathrm{f}}^{1965}}(0.5)$.[5] The function $\mathrm{g}$ is defined by $\mathrm{g}:x\mapsto \sqrt{4+2x},\quad x\in \mathbb{R},\ \ 0\le xSketch the graph of $y=\mathrm{g}(x)$. Your sketch should indicate the coordinates of the end-points.[2] On the same diagram of part (i), sketch the graph of $y={{\mathrm{g}}^{-1}}(x)$, showing the relationship between $\mathrm{g}$and ${{\mathrm{g}}^{-1}}$.[2] Find the values of $x$ satisfying the equation ${{\mathrm{g}}^{-1}}\mathrm{g}(x)=\mathrm{g}{{\mathrm{g}}^{-1}}(x)$.[1]

Accepted Answer

(a) $f^{-1}: x \mapsto \frac{2x-1}{2x-2}, x < 1$; $f^{1965}(0.5) = 0$ (b)(iii) $2 \leq x < 6$

2013 NYJC P2 Q2

2013 NYJC P2 Q2

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