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What are the condition for the existence of an inverse trigonometric function?
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NOTE: The The graphs of $y=f(x)$ and $y=f^{-1}(x)$ are symmetrical about the line $y=x$.

For the inverse function to exist we need the original function to be ONE-TO-ONE. So it must pass the "Horizontal Line Test" i.e. a horizontal line must not cut the graph more than once.

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