Question
Give an example of a one-to-one, onto function $f:[0,1] \rightarrow[0,1]$ that is not monotone. Can you find a monotone, one-to-one function that is not onto? Or a monotone, onto function that is not one-to-one?
Step 1
One such function is defined as follows: \[ f(x) = \begin{cases} 2x & \text{if } 0 \leq x < 0.5 \\ 2 - 2x & \text{if } 0.5 \leq x \leq 1 \end{cases} \] Show more…
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