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\includegraphics[max width=\textwidth, alt={}, center]{5c501214-b41c-43a8-b9c6-986758e83e7d-4_534_935_264_605}
The function f is defined for the domain \(x \geqslant 0\) by
$$f ( x ) = \frac { 15 x } { x ^ { 2 } + 5 }$$
The diagram shows the curve with equation \(y = \mathrm { f } ( x )\).
- Find the range of f .
- The function g is defined for the domain \(x \geqslant k\) by
$$\mathrm { g } ( x ) = \frac { 15 x } { x ^ { 2 } + 5 }$$
Given that g is a one-one function, state the least possible value of \(k\).
- Show that there is no point on the curve \(y = \mathrm { g } ( x )\) at which the gradient is - 1 .