A function $\mathrm{f}\left( x \right)$is said to be strictly increasing if for any numbers $a,b\in {{\mathrm{D}}_{\mathrm{f}}}$,
$a < b\Leftrightarrow \mathrm{f}\left( a \right) < \mathrm{f}\left( b \right)$.
Prove that if the function $\mathrm{f}\left( x \right)$ is strictly increasing, then so is ${{\mathrm{f}}^{-1}}\left( x \right)$.

A function $\mathrm{f}\left( x \right)$is said to be strictly increasing if for any numbers $a,b\in {{\mathrm{D}}_{\mathrm{f}}}$,

$a < b\Leftrightarrow \mathrm{f}\left( a \right) < \mathrm{f}\left( b \right)$.

Prove that if the function $\mathrm{f}\left( x \right)$ is strictly increasing, then so is ${{\mathrm{f}}^{-1}}\left( x \right)$.

One-to-One Functions and Inverse Existence

Functions

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Proving That An Inverse Function Is Strictly Increasing When Function Is Strictly Increasing

Proving That An Inverse Function Is Strictly Increasing When Function Is Strictly Increasing

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