Inverse Function | Characteristics: EXTRA: Median, Sequences, Mediant Inequality Proof....p8

In this video, part 8 of the series: Inverse Function and its Characteristics.

EXTRA: Studying, division property of exponents holds for all real number exponents, namely for f(x) = e^x.

Specifically, discusses the median, sequences of rational numbers, then the mediant inequality including a proof, along with examples. Essentially scratch-work for the proof for irrational exponents.

Which helps to demonstrate, if f(x) = e^x is continuous and injective, that guarantees it has an inverse, *and the inverse will be continuous.