10 The function f is defined by
$$f ( x ) = \frac { x ^ { 2 } + 10 } { 2 x + 5 }$$
where \(f\) has its maximum possible domain.
The curve \(y = \mathrm { f } ( x )\) intersects the line \(y = x\) at the points \(P\) and \(Q\) as shown below.
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10
- State the value of \(x\) which is not in the domain of f .
10
- Explain how you know that the function f is many-to-one.
10 - Show that the \(x\)-coordinates of \(P\) and \(Q\) satisfy the equation
$$x ^ { 2 } + 5 x - 10 = 0$$
[2 marks]
10
- (ii) Hence, find the exact \(x\)-coordinate of \(P\) and the exact \(x\)-coordinate of \(Q\).
10 - Show that \(P\) and \(Q\) are stationary points of the curve.
Fully justify your answer.
10 - Using set notation, state the range of f .