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Restricting a quadratic mapping

Restricting a quadratic mapping

4 marks
TGM Original
The rule f(x)=(x-3)2+2 initially has domain R. Explain why it has no inverse function. Its domain is then restricted to x >= k. Find the least possible k for which an inverse exists, and state the range for that value.

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Answer:No inverse on \(\mathbb R\); least \(k=3\), range \([2,\infty)\).

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