14. Given that
$$y = \frac { \left( x ^ { 2 } - 4 \right) ^ { \frac { 1 } { 2 } } } { x ^ { 3 } } \quad x > 2$$
- show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { A x ^ { 2 } + 12 } { x ^ { 4 } \left( x ^ { 2 } - 4 \right) ^ { \frac { 1 } { 2 } } } \quad x > 2$$
where \(A\) is a constant to be found.
\begin{figure}[h]
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\caption{Figure 4}
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Figure 4 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = \frac { 24 \left( x ^ { 2 } - 4 \right) ^ { \frac { 1 } { 2 } } } { x ^ { 3 } } \quad x > 2$$ - Use your answer to part (a) to find the range of f.
- State a reason why f-1 does not exist.