]> 1.4 Standard functions

## 1.4 Standard Functions

A standard function is one defined on an interval of $ℝ$ that is obtained by a finite sequence of standard operations starting from any combination of three basic functions .

What are the basic functions ?

The identity function $f ( x ) = x$

The exponential function $f ( x ) = exp ⁡ ( x )$

The sine function $f ( x ) = sin ⁡ ( x )$

What are the standard operations?

Multiplication by a number in $ℝ$ , addition, subtraction, multiplication, division, substitution of the value of one function as argument of another, and taking the "inverse".

Most of the functions we encounter will be standard functions.

Examples: $4 x 2$ , $x sin ⁡ ( x )$ , $exp ⁡ ( sin ⁡ x ) x$ .

You can enter your favorite standard functions, $f$ and $g$ , in the following applet, and observe the effects of combining $f$ and $g$ in various ways, and also look at the inverse function to $f$ .

Note that when f has the same value for more than one argument, you must decide which of these arguments you want to call the value of the inverse function.