If the inverse function of f exists, f^-1, does that mean f must

Can you repeat the question?

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>>231035
>>231033
>>231031

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No. A strictly monotone function is always injective, however.

For example, the function
f(x) = {x when x< -1
{2+x^2 when x >= -1 > 0
{4+x^2 when x>=0
is injective but not monotone.
However, if f(x) is continuous, then it must also be strictly monotone to be injective.

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>>231040
Hmm. So for this I could say that since f is continuous and injective (the no value repeats part), is must be strictly monotone?

>>231042
It's certainly true but whether that's enough depends on what level of rigor is expected of you.

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>>231047
Ok, I'm sure there is a proper way of showing this with actual math, but I'll just say it in words and hope it's worth something. Thanks for the help.