relationship between a function and its inverse

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I did some observation about a function and its inverse and I would like to confirm whether these observation are true:

1. The domain and range roles of the inverse and function are 'exchanged'
2. The graph of inverse function is flipped 90degree as compared to the function.
3. x is treated like y, y is treated like x in its inverse.

is it always the case?

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2 Answers

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Your sentences are true except 2nd one: the function $f$ and its inverse $f^{-1}$ are symmetrical with respect to the line $y=x$. It follows directly from your 3rd point.

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Number 1 and 3 are correct but it's not that it gets rotated 90 degrees, the inverse is a reflection over the line y=X from the parent function.

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