The graph of the function \(y = \mathrm { f } ( x )\) passes through the point \(P\) with coordinates (2, 6), and is a one-one function. State the coordinates of the point corresponding to \(P\) on each of the following curves.
\(\quad y = \mathrm { f } ( x ) + 3\)
\(\quad y = 2 \mathrm { f } ( 3 x - 1 )\)
\(y = \mathrm { f } ^ { - 1 } ( x )\)
\includegraphics[max width=\textwidth, alt={}, center]{6b766f5c-8533-4e0c-bb10-0d9949dc777b-5_494_739_806_333}
The diagram shows part of the graph of \(y = \mathrm { g } ^ { \prime } ( x )\). This is the graph of the gradient function of \(y = \mathrm { g } ( x )\). The graph intersects the \(x\)-axis at \(x = - 2\) and \(x = 4\).
State the \(x\)-coordinate of any stationary points on the graph of \(y = \mathrm { g } ( x )\).
State the set of values of \(x\) for which \(y = \mathrm { g } ( x )\) is a decreasing function.
State the \(x\)-coordinate of any points of inflection on the graph of \(y = \mathrm { g } ( x )\).