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Let $$f \colon A \rightarrow B$$ be a function defined as $$f(x) = (x^2 - 4x + 4)^{1/2}$$ where $$A$$ and $$B$$ are subsets of $$\mathbb{R}$$. Then find the largest possible subset $$A$$ of $$\mathbb{R}^+$$ such that $$f$$ is bijective and find the corresponding $$B$$.
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is a pair of sets. $$f(x) = \sqrt{(x - 2)^2} = |x - 2|$$, which is one-one on $$[2, \infty)$$, where it equals $$x - 2$$ and takes every value in $$[0, \infty)$$. So $$A = [2, \infty)$$ and $$B = [0, \infty)$$.
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