2013 NYJC P2 Q2
(a)
The function $\text{f}$ is defined by
$\text{f}:x\mapsto \frac{2x-1}{2x-2},\quad x<1$.
Define ${{\text{f}}^{-1}}$ in a similar form. Hence or otherwise find ${{\text{f}}^{2}}(x)$ and state the value of ${{\text{f}}^{1965}}(0.5)$.
[5]
(b)
The function $\text{g}$ is defined by
$\text{g}:x\mapsto \sqrt{4+2x},\quad x\in \mathbb{R},\ \ 0\le x<16.$
(i) Sketch the graph of $y=\text{g}(x)$. Your sketch should indicate the coordinates of the end-points.
[2]
(ii) On the same diagram of part (i), sketch the graph of $y={{\text{g}}^{-1}}(x)$, showing the relationship between $\text{g}$and ${{\text{g}}^{-1}}$.
[2]
(iii) Find the values of $x$ satisfying the equation ${{\text{g}}^{-1}}\text{g}(x)=\text{g}{{\text{g}}^{-1}}(x)$.
[1]
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