16 Curve \(C\) has equation \(y = \frac { a x } { x + b }\) where \(a\) and \(b\) are constants.
The equations of the asymptotes to \(C\) are \(x = - 2\) and \(y = 3\)
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16
- Write down the value of \(a\) and the value of \(b\)
16
- The gradient of \(C\) at the origin is \(\frac { 3 } { 2 }\)
With reference to the graph, explain why there is exactly one root of the equation
$$\frac { a x } { x + b } = \frac { 3 x } { 2 }$$
16
- Using the values found in part (a), solve the inequality
$$\frac { a x } { x + b } \leq 1 - x$$
[4 marks]