1.
$$g ( x ) = \frac { 6 x + 12 } { x ^ { 2 } + 3 x + 2 } - 2 , \quad x \geqslant 0$$
- Show that \(\mathrm { g } ( x ) = \frac { 4 - 2 x } { x + 1 } , x \geqslant 0\)
- \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0f6fd881-4d4b-4f80-96cc-6da41cc33c60-02_494_922_628_511}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve with equation \(y = \mathrm { g } ( x ) , x \geqslant 0\)
The curve meets the \(y\)-axis at \(( 0,4 )\) and crosses the \(x\)-axis at \(( 2,0 )\).
On separate diagrams sketch the graph with equation
- \(y = 2 \mathrm {~g} ( 2 x )\),
- \(y = \mathrm { g } ^ { - 1 } ( x )\).
Show on each sketch the coordinates of each point at which the graph meets or crosses the axes.