9709 - 8 marks | Maths4U

A variable endpoint controls the inverse

8 written marks

Let \(f(x)=x^2-4x+1\) on the non-degenerate interval \([a,6]\), where \(a<6\).

Find all \(a\) for which \(f\) is one-one.

Take \(a=4\). Find \(f^{-1}\), with its domain and range.

Find all \(a\) such that \(f\) is one-one AND \(f^{-1}\) is defined for every input in \([1,13]\).

Complete-answer checking, worked solutions and indicative written criteria.