3 The function \(\mathrm { f } ( x )\) is given by \(\mathrm { f } ( x ) = ( 1 - a x ) ^ { - 3 }\), where \(a\) is a non-zero constant. In the binomial expansion of \(\mathrm { f } ( x )\), the coefficients of \(x\) and \(x ^ { 2 }\) are equal.
- Find the value of \(a\).
- Using this value for \(a\),
- state the set of values of \(x\) for which the binomial expansion is valid,
- write down the quadratic function which approximates \(\mathrm { f } ( x )\) when \(x\) is small.