4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64f015bf-29fb-4374-af34-3745ea49aced-05_945_1026_269_466}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with equation
$$y = \frac { 1 } { x } + 1 , \quad x \neq 0$$
The curve \(C\) crosses the \(x\)-axis at the point \(A\).
- State the \(x\) coordinate of the point \(A\).
The curve \(D\) has equation \(y = x ^ { 2 } ( x - 2 )\), for all real values of \(x\).
- A copy of Figure 1 is shown on page 7.
On this copy, sketch a graph of curve \(D\).
Show on the sketch the coordinates of each point where the curve \(D\) crosses the coordinate axes. - Using your sketch, state, giving a reason, the number of real solutions to the equation
$$x ^ { 2 } ( x - 2 ) = \frac { 1 } { x } + 1$$
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64f015bf-29fb-4374-af34-3745ea49aced-06_942_1026_516_466}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}