6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fa4afaf4-fe5d-4f3a-b3de-9600d5502a49-12_728_1086_246_493}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the graph of \(y = \mathrm { g } ( x )\), where
$$g ( x ) = \begin{cases} ( x - 2 ) ^ { 2 } + 1 & x \leqslant 2
4 x - 7 & x > 2 \end{cases}$$
- Find the value of \(\operatorname { gg } ( 0 )\).
- Find all values of \(x\) for which
$$\mathrm { g } ( x ) > 28$$
The function h is defined by
$$\mathrm { h } ( x ) = ( x - 2 ) ^ { 2 } + 1 \quad x \leqslant 2$$
- Explain why h has an inverse but g does not.
- Solve the equation
$$\mathrm { h } ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$$