4.
The functions \(f\) and \(g\) are defined by
$$\begin{array} { l l l }
\mathrm { f } ( x ) = \frac { k x } { 2 x - 1 } & x \in \mathbb { R } & x \neq \frac { 1 } { 2 }
\mathrm {~g} ( x ) = 2 + 3 x - x ^ { 2 } & x \in \mathbb { R } &
\end{array}$$
where \(k\) is a non-zero constant.
- Find in terms of \(k\)
- \(\mathrm { fg } ( 4 )\)
- the range of f
- \(\mathrm { f } ^ { - 1 }\)
Given that
$$\mathrm { f } ^ { - 1 } ( 2 ) = \frac { 11 } { 3 \mathrm {~g} ( 2 ) }$$
- find the exact value of \(k\)
[0pt]
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