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When does an inverse exist?

When does an inverse exist? · Diagrams

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Base two exponential and logarithm

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Equal-scale y=2^x and y=log₂x reflect in y=x, with points(0,1),(1,0),(1,2),(2,1) and asymptotes y=0,x=0. Source bases 2,e exceed 1; logarithms with bases between 0,1 decrease.
Equal-scale y=2^x and y=log₂x reflect in y=x, with points(0,1),(1,0),(1,2),(2,1) and asymptotes y=0,x=0. Source bases 2,e exceed 1; logarithms with bases between 0,1 decrease.
Equal-scale y=2^x and y=log₂x reflect in y=x, with points(0,1),(1,0),(1,2),(2,1) and asymptotes y=0,x=0. Source bases 2,e exceed 1; logarithms with bases between 0,1 decrease.
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