3 The functions f and g are defined for \(x \in \mathbb { R }\) by
$$\begin{aligned}
& \mathrm { f } : x \mapsto 4 x - 2 x ^ { 2 }
& \mathrm {~g} : x \mapsto 5 x + 3
\end{aligned}$$
- Find the range of f .
- Find the value of the constant \(k\) for which the equation \(\mathrm { gf } ( x ) = k\) has equal roots.
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In the diagram, \(A\) is the point \(( - 1,3 )\) and \(B\) is the point \(( 3,1 )\). The line \(L _ { 1 }\) passes through \(A\) and is parallel to \(O B\). The line \(L _ { 2 }\) passes through \(B\) and is perpendicular to \(A B\). The lines \(L _ { 1 }\) and \(L _ { 2 }\) meet at \(C\). Find the coordinates of \(C\).