Exponential Function

math

Definition

Exponential Function

An exponential function is a function where the function’s parameters are exponents.

Examples:

• $f(x)=e^x$
• $f(x)=a^x$ with $a\in {\mathbb{R}}^{+}$

Bijectivity

The exponential function is bijective from $\mathbb{R}$ to ${\mathbb{R}}^{+}$.

Continuity

Continuity of Exponential Functions

Exponential functions of form

$$f(x)=e^x,f(x)=a^x$$

with $e$ being the Euler’s number and $a>0$ are continuous.