Question 6
Let \(f(x)=x^2-4x+7\), \(x\ge2\), and \(g(x)=x+k\), \(x\in\mathbb R\). Let \(h=fg\) be formed after restricting the domain of \(g\) as little as possible.
Find the rule and domain of \(h\), in terms of \(k\).
Given \(h^{-1}(7)=1\), find \(k\), and then find \(h^{-1}\) with its domain.
Complete-answer checking, worked solutions and indicative written criteria.
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