Exponential is Strictly Increasing

Theorem
Let $x \in \R$ be a real number.

Let $\exp x$ be the exponential of $x$.

Then:
 * The function $f \left({x}\right) = \exp x$ is strictly increasing and convex.

Proof
By definition, the exponential function is the inverse of the natural logarithm function.

From Logarithm is Strictly Increasing and Concave, $\ln x$ is strictly increasing and concave.

The result follows from Inverse of Strictly Increasing Concave Real Function is Convex.