Elementary Function

analysis

Definition

Elementary Function

Functions, that only consist of polynomial functions, logarithmic functions, exponential functions, trigonometric functions, inverse trigonometric functions, the basic arithmetic operations, and function compositions are called elementary functions.

Continuity

Let $f(x)$ and $g(x)$ continuous functions. Then, on suitable domains of definition, the following functions are also continuous:

• $f(x)\pm g(x)$
• $f(x)g(x)$
• $\frac{f(x)}{g(x)}$, $g(x)\ne 0$
• $f(g(x))$

From that, the following follows:

Continuity of Elementary Functions

Elementary functions are always continuous.