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If the inverse of is a continuous function, why must the function be either strictly increasing or decreasing? Sketch an example to support your reasoning.

Strictly increasing means, as increases, -values are always going up.
Strictly decreasing means, as  increases, -values are always going down.

If a function is NOT strictly increasing or decreasing, then either.
I. it oscillates between increasing and decreasing.
II. it is horizontal always or sometimes.

As you sketch, try to find a counter-example to this statement. In other words, try to sketch a function with a continuous inverse function that is NOT strictly increasing or strictly decreasing.

Note that and its inverse must both be continuous AND both be functions.