Inverse of Strictly Monotone Continuous Real Function is Strictly Monotone and Continuous/Examples

Examples of Use of Inverse of Strictly Monotone Continuous Real Function is Strictly Monotone and Continuous

Arbitrary Example

Consider the real function:

$\forall x \in \closedint 0 1: \map f x = y = 2 x + 3$

This has an inverse:

$\map {f^{-1} } y = x = \dfrac {y - 3} 2$

on the closed interval $\closedint 3 5$

Hence we can say:

$f: x \mapsto 2 x + 3$ on $\closedint 0 1$

and:

$f^{-1}: x \mapsto \dfrac {x - 3} 2$ on $\closedint 3 5$