Category:Inverse of Strictly Monotone Continuous Real Function is Strictly Monotone and Continuous

This category contains pages concerning Inverse of Strictly Monotone Continuous Real Function is Strictly Monotone and Continuous:

Let $f$ be a continuous real function which is defined on the closed interval $I := \closedint a b$.

Let $f$ be strictly monotone on $I$.

Then $f$ has an inverse function $f^{-1}$ which is continuous and strictly monotone on $f \sqbrk I$.