
A standard function is one defined on an interval of $\mathbb{R}$ 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 $f(x)=\mathrm{exp}(x)$
The sine function $f(x)=\mathrm{sin}(x)$
What are the standard operations?
Multiplication by a number in $\mathbb{R}$ , 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: $4{x}^{2}$ , $x\mathrm{sin}(x)$ , $\frac{\mathrm{exp}(\mathrm{sin}x)}{x}$ .
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.
