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When does an inverse exist?

When does an inverse exist? · Diagrams

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A restriction keeps the rule and changes the domain

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Full parabola (x+2)² has vertex (−2,0), y-intercept 4; restriction x>−2 retains only its increasing right branch with an open vertex. Same rule, smaller domain; full curve extends the restricted one.
Full parabola (x+2)² has vertex (−2,0), y-intercept 4; restriction x>−2 retains only its increasing right branch with an open vertex. Same rule, smaller domain; full curve extends the restricted one.
Full parabola (x+2)² has vertex (−2,0), y-intercept 4; restriction x>−2 retains only its increasing right branch with an open vertex. Same rule, smaller domain; full curve extends the restricted one.
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