9 Answer parts (i) and (iii) on the insert provided.
Fig. 9 shows a sketch graph of \(y = \mathrm { f } ( x )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3f8be5ab-d241-4027-af26-c49da9394adc-4_401_799_488_593}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{figure}
- On the Insert sketch graphs of
(A) \(y = 2 \mathrm { f } ( x )\),
(B) \(y = \mathrm { f } ( - x )\),
(C) \(y = \mathrm { f } ( x - 2 )\)
In each case describe the transformations. - Explain why the function \(y = \mathrm { f } ( x )\) does not have an inverse function.
- The function \(\mathrm { g } ( x )\) is defined as follows:
$$\mathrm { g } ( x ) = \mathrm { f } ( x ) \text { for } x \geq 0$$
On the Insert sketch the graph of \(y = \mathrm { g } ^ { - 1 } ( x )\).
- You are given that \(\mathrm { f } ( x ) = x ^ { 2 } ( x + 2 )\).
Calculate the gradient of the curve \(y = \mathrm { f } ( x )\) at the point \(( 1,3 )\).
Deduce the gradient of the function \(\mathrm { g } ^ { - 1 } ( x )\) at the point where \(x = 3\). - Show that \(\mathrm { g } ( x )\) and \(\mathrm { g } ^ { - 1 } ( x )\) cross where \(x = - 1 + \sqrt { 2 }\).
\section*{Insert for question 9.}
- (A) On the axes below sketch the graph of \(y = 2 \mathrm { f } ( x )\).
Describe the transformation.
\includegraphics[max width=\textwidth, alt={}, center]{3f8be5ab-d241-4027-af26-c49da9394adc-5_563_1102_484_395}
Description: - (B) On the axes below sketch the graph of \(y = \mathrm { f } ( - x )\).
Describe the transformation.
\includegraphics[max width=\textwidth, alt={}, center]{3f8be5ab-d241-4027-af26-c49da9394adc-5_588_1154_1576_404}
Description: - (C) On the axes below sketch the graph of \(y = \mathrm { f } ( x - 2 )\).
Describe the transformation.
\includegraphics[max width=\textwidth, alt={}, center]{3f8be5ab-d241-4027-af26-c49da9394adc-6_615_1230_402_406}
Description: - The function \(\mathrm { g } ( x )\) is defined as follows:
$$\mathrm { g } ( x ) = \mathrm { f } ( x ) \text { for } x \geq 0$$
On the axes below sketch the graph of \(y = g ^ { - 1 } ( x )\).
\includegraphics[max width=\textwidth, alt={}, center]{3f8be5ab-d241-4027-af26-c49da9394adc-6_677_1356_1567_312}